TSTP Solution File: NUM600+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NUM600+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 01:30:50 EDT 2024

% Result   : Theorem 90.58s 36.86s
% Output   : Refutation 91.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :  145
% Syntax   : Number of formulae    :  980 ( 156 unt;  48 typ;   0 def)
%            Number of atoms       : 3203 (1104 equ;   0 cnn)
%            Maximal formula atoms :   22 (   3 avg)
%            Number of connectives : 8763 (1336   ~;1156   |; 350   &;5552   @)
%                                         (  22 <=>; 347  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   58 (  58   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   51 (  48 usr;  16 con; 0-3 aty)
%            Number of variables   :  829 (   0   ^ 798   !;  31   ?; 829   :)

% Comments : 
%------------------------------------------------------------------------------
thf(slcrc0_type,type,
    slcrc0: $i ).

thf(aSet0_type,type,
    aSet0: $i > $o ).

thf(aElementOf0_type,type,
    aElementOf0: $i > $i > $o ).

thf(aSubsetOf0_type,type,
    aSubsetOf0: $i > $i > $o ).

thf(aElement0_type,type,
    aElement0: $i > $o ).

thf(sdtpldt0_type,type,
    sdtpldt0: $i > $i > $i ).

thf(sdtmndt0_type,type,
    sdtmndt0: $i > $i > $i ).

thf(szNzAzT0_type,type,
    szNzAzT0: $i ).

thf(szmzizndt0_type,type,
    szmzizndt0: $i > $i ).

thf(sdtlseqdt0_type,type,
    sdtlseqdt0: $i > $i > $o ).

thf(isFinite0_type,type,
    isFinite0: $i > $o ).

thf(szmzazxdt0_type,type,
    szmzazxdt0: $i > $i ).

thf(slbdtrb0_type,type,
    slbdtrb0: $i > $i ).

thf(szszuzczcdt0_type,type,
    szszuzczcdt0: $i > $i ).

thf(slbdtsldtrb0_type,type,
    slbdtsldtrb0: $i > $i > $i ).

thf(sbrdtbr0_type,type,
    sbrdtbr0: $i > $i ).

thf(aFunction0_type,type,
    aFunction0: $i > $o ).

thf(sdtlbdtrb0_type,type,
    sdtlbdtrb0: $i > $i > $i ).

thf(szDzozmdt0_type,type,
    szDzozmdt0: $i > $i ).

thf(sdtlpdtrp0_type,type,
    sdtlpdtrp0: $i > $i > $i ).

thf(sdtlcdtrc0_type,type,
    sdtlcdtrc0: $i > $i > $i ).

thf(sdtexdt0_type,type,
    sdtexdt0: $i > $i > $i ).

thf(xO_type,type,
    xO: $i ).

thf(xd_type,type,
    xd: $i ).

thf(szDzizrdt0_type,type,
    szDzizrdt0: $i > $i ).

thf(xe_type,type,
    xe: $i ).

thf(sz00_type,type,
    sz00: $i ).

thf(xc_type,type,
    xc: $i ).

thf(xS_type,type,
    xS: $i ).

thf(xK_type,type,
    xK: $i ).

thf(xT_type,type,
    xT: $i ).

thf(isCountable0_type,type,
    isCountable0: $i > $o ).

thf(xN_type,type,
    xN: $i ).

thf(iLess0_type,type,
    iLess0: $i > $i > $o ).

thf(xk_type,type,
    xk: $i ).

thf(xC_type,type,
    xC: $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i > $i > $o ).

thf(sk3_type,type,
    sk3: $i > $i > $i ).

thf(sk4_type,type,
    sk4: $i > $i > $i ).

thf(sk5_type,type,
    sk5: $i > $i > $i ).

thf(sk6_type,type,
    sk6: $i > $i > $i ).

thf(sk7_type,type,
    sk7: $i > $i ).

thf(sk8_type,type,
    sk8: $i > $i > $i > $o ).

thf(sk9_type,type,
    sk9: $i > $i > $i > $i ).

thf(sk10_type,type,
    sk10: $i > $i > $i > $i ).

thf(sk11_type,type,
    sk11: $i > $i > $i > $i ).

thf(sk31_type,type,
    sk31: $i > $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ xO )
     => ? [B: $i] :
          ( ( aElementOf0 @ B @ szNzAzT0 )
          & ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
          & ( ( sdtlpdtrp0 @ xe @ B )
            = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( aElementOf0 @ A @ xO )
       => ? [B: $i] :
            ( ( aElementOf0 @ B @ szNzAzT0 )
            & ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
            & ( ( sdtlpdtrp0 @ xe @ B )
              = A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(99,plain,
    ~ ! [A: $i] :
        ( ( aElementOf0 @ A @ xO )
       => ? [B: $i] :
            ( ( aElementOf0 @ B @ szNzAzT0 )
            & ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
            & ( ( sdtlpdtrp0 @ xe @ B )
              = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(101,plain,
    aElementOf0 @ sk1 @ xO,
    inference(cnf,[status(esa)],[99]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
        & ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).

thf(216,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
        & ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(218,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ),
    inference(cnf,[status(esa)],[216]) ).

thf(20041,plain,
    ! [A: $i] :
      ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[101,218]) ).

thf(20169,plain,
    ! [A: $i] :
      ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( sk1 != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[20041]) ).

thf(20194,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ sk1 ) )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[20169]) ).

thf(81,axiom,
    ( ( aElementOf0 @ xk @ szNzAzT0 )
    & ( ( szszuzczcdt0 @ xk )
      = xK ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).

thf(506,plain,
    ( ( aElementOf0 @ xk @ szNzAzT0 )
    & ( ( szszuzczcdt0 @ xk )
      = xK ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(508,plain,
    aElementOf0 @ xk @ szNzAzT0,
    inference(cnf,[status(esa)],[506]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( A = sz00 )
        | ? [B: $i] :
            ( ( aElementOf0 @ B @ szNzAzT0 )
            & ( A
              = ( szszuzczcdt0 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).

thf(513,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( A = sz00 )
        | ? [B: $i] :
            ( ( aElementOf0 @ B @ szNzAzT0 )
            & ( A
              = ( szszuzczcdt0 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(515,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 ) ),
    inference(cnf,[status(esa)],[513]) ).

thf(517,plain,
    ! [A: $i] :
      ( ( A = sz00 )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 ) ),
    inference(lifteq,[status(thm)],[515]) ).

thf(872,plain,
    ! [A: $i] :
      ( ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,517]) ).

thf(873,plain,
    ( ( xk = sz00 )
    | ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[872:[bind(A,$thf( xk ))]]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( B
            = ( slbdtrb0 @ A ) )
        <=> ( ( aSet0 @ B )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ B )
              <=> ( ( aElementOf0 @ C @ szNzAzT0 )
                  & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).

thf(168,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( B
              = ( slbdtrb0 @ A ) )
           => ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( ( aElementOf0 @ C @ B )
                   => ( ( aElementOf0 @ C @ szNzAzT0 )
                      & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
                  & ( ( ( aElementOf0 @ C @ szNzAzT0 )
                      & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
                   => ( aElementOf0 @ C @ B ) ) ) ) )
          & ( ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( ( aElementOf0 @ C @ B )
                   => ( ( aElementOf0 @ C @ szNzAzT0 )
                      & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
                  & ( ( ( aElementOf0 @ C @ szNzAzT0 )
                      & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
                   => ( aElementOf0 @ C @ B ) ) ) )
           => ( B
              = ( slbdtrb0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(169,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ! [B: $i] :
            ( ( B
              = ( slbdtrb0 @ A ) )
           => ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ B )
                 => ( ( aElementOf0 @ C @ szNzAzT0 )
                    & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
              & ! [C: $i] :
                  ( ( ( aElementOf0 @ C @ szNzAzT0 )
                    & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
                 => ( aElementOf0 @ C @ B ) ) ) )
        & ! [B: $i] :
            ( ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ B )
                 => ( ( aElementOf0 @ C @ szNzAzT0 )
                    & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
              & ! [C: $i] :
                  ( ( ( aElementOf0 @ C @ szNzAzT0 )
                    & ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
                 => ( aElementOf0 @ C @ B ) ) )
           => ( B
              = ( slbdtrb0 @ A ) ) ) ) ),
    inference(miniscope,[status(thm)],[168]) ).

thf(176,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( B
       != ( slbdtrb0 @ A ) )
      | ( aSet0 @ B ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(185,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( aSet0 @ B ) ),
    inference(lifteq,[status(thm)],[176]) ).

thf(186,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( aSet0 @ ( slbdtrb0 @ A ) ) ),
    inference(simp,[status(thm)],[185]) ).

thf(7765,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[873,186]) ).

thf(7766,plain,
    ( ( xk = sz00 )
    | ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ),
    inference(pattern_uni,[status(thm)],[7765:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(76,axiom,
    ( ( aSubsetOf0 @ xS @ szNzAzT0 )
    & ( isCountable0 @ xS ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).

thf(455,plain,
    ( ( aSubsetOf0 @ xS @ szNzAzT0 )
    & ( isCountable0 @ xS ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(457,plain,
    aSubsetOf0 @ xS @ szNzAzT0,
    inference(cnf,[status(esa)],[455]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( A != slcrc0 ) )
     => ! [B: $i] :
          ( ( B
            = ( szmzizndt0 @ A ) )
        <=> ( ( aElementOf0 @ B @ A )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ A )
               => ( sdtlseqdt0 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).

thf(241,plain,
    ! [A: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( A != slcrc0 ) )
     => ! [B: $i] :
          ( ( ( B
              = ( szmzizndt0 @ A ) )
           => ( ( aElementOf0 @ B @ A )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ A )
                 => ( sdtlseqdt0 @ B @ C ) ) ) )
          & ( ( ( aElementOf0 @ B @ A )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ A )
                 => ( sdtlseqdt0 @ B @ C ) ) )
           => ( B
              = ( szmzizndt0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(242,plain,
    ! [A: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( A != slcrc0 ) )
     => ( ! [B: $i] :
            ( ( B
              = ( szmzizndt0 @ A ) )
           => ( ( aElementOf0 @ B @ A )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ A )
                 => ( sdtlseqdt0 @ B @ C ) ) ) )
        & ! [B: $i] :
            ( ( ( aElementOf0 @ B @ A )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ A )
                 => ( sdtlseqdt0 @ B @ C ) ) )
           => ( B
              = ( szmzizndt0 @ A ) ) ) ) ),
    inference(miniscope,[status(thm)],[241]) ).

thf(244,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ( A = slcrc0 )
      | ( B
       != ( szmzizndt0 @ A ) )
      | ( aElementOf0 @ B @ A ) ),
    inference(cnf,[status(esa)],[242]) ).

thf(249,plain,
    ! [B: $i,A: $i] :
      ( ( A = slcrc0 )
      | ( B
       != ( szmzizndt0 @ A ) )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ( aElementOf0 @ B @ A ) ),
    inference(lifteq,[status(thm)],[244]) ).

thf(250,plain,
    ! [A: $i] :
      ( ( A = slcrc0 )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ( aElementOf0 @ ( szmzizndt0 @ A ) @ A ) ),
    inference(simp,[status(thm)],[249]) ).

thf(30071,plain,
    ! [A: $i] :
      ( ( A = slcrc0 )
      | ( aElementOf0 @ ( szmzizndt0 @ A ) @ A )
      | ( ( aSubsetOf0 @ xS @ szNzAzT0 )
       != ( aSubsetOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[457,250]) ).

thf(30072,plain,
    ( ( xS = slcrc0 )
    | ( aElementOf0 @ ( szmzizndt0 @ xS ) @ xS ) ),
    inference(pattern_uni,[status(thm)],[30071:[bind(A,$thf( xS ))]]) ).

thf(456,plain,
    isCountable0 @ xS,
    inference(cnf,[status(esa)],[455]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isCountable0 @ A ) )
     => ( A != slcrc0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).

thf(123,plain,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isCountable0 @ A ) )
     => ( A != slcrc0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(124,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isCountable0 @ A )
      | ( A != slcrc0 ) ),
    inference(cnf,[status(esa)],[123]) ).

thf(125,plain,
    ! [A: $i] :
      ( ( A != slcrc0 )
      | ~ ( aSet0 @ A )
      | ~ ( isCountable0 @ A ) ),
    inference(lifteq,[status(thm)],[124]) ).

thf(126,plain,
    ( ~ ( aSet0 @ slcrc0 )
    | ~ ( isCountable0 @ slcrc0 ) ),
    inference(simp,[status(thm)],[125]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( A = slcrc0 )
    <=> ( ( aSet0 @ A )
        & ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

thf(364,plain,
    ! [A: $i] :
      ( ( ( A = slcrc0 )
       => ( ( aSet0 @ A )
          & ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) )
      & ( ( ( aSet0 @ A )
          & ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
       => ( A = slcrc0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(365,plain,
    ( ! [A: $i] :
        ( ( A = slcrc0 )
       => ( ( aSet0 @ A )
          & ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) )
    & ! [A: $i] :
        ( ( ( aSet0 @ A )
          & ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
       => ( A = slcrc0 ) ) ),
    inference(miniscope,[status(thm)],[364]) ).

thf(367,plain,
    ! [A: $i] :
      ( ( A != slcrc0 )
      | ( aSet0 @ A ) ),
    inference(cnf,[status(esa)],[365]) ).

thf(371,plain,
    ! [A: $i] :
      ( ( A != slcrc0 )
      | ( aSet0 @ A ) ),
    inference(lifteq,[status(thm)],[367]) ).

thf(372,plain,
    aSet0 @ slcrc0,
    inference(simp,[status(thm)],[371]) ).

thf(646,plain,
    ( ~ $true
    | ~ ( isCountable0 @ slcrc0 ) ),
    inference(rewrite,[status(thm)],[126,372]) ).

thf(647,plain,
    ~ ( isCountable0 @ slcrc0 ),
    inference(simp,[status(thm)],[646]) ).

thf(659,plain,
    ( ( isCountable0 @ xS )
   != ( isCountable0 @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[456,647]) ).

thf(660,plain,
    xS != slcrc0,
    inference(simp,[status(thm)],[659]) ).

thf(34726,plain,
    aElementOf0 @ ( szmzizndt0 @ xS ) @ xS,
    inference(simplifyReflect,[status(thm)],[30072,660]) ).

thf(16,axiom,
    ( ( slbdtrb0 @ sz00 )
    = slcrc0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).

thf(136,plain,
    ( ( slbdtrb0 @ sz00 )
    = slcrc0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(137,plain,
    ( ( slbdtrb0 @ sz00 )
    = slcrc0 ),
    inference(lifteq,[status(thm)],[136]) ).

thf(7762,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[101,186]) ).

thf(7807,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( sk1 != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[7762]) ).

thf(7814,plain,
    ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[7807]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( aSubsetOf0 @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).

thf(134,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( aSubsetOf0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(135,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ( aSubsetOf0 @ A @ A ) ),
    inference(cnf,[status(esa)],[134]) ).

thf(8218,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7814,135]) ).

thf(8219,plain,
    ( ( xO != szNzAzT0 )
    | ( aSubsetOf0 @ ( slbdtrb0 @ sk1 ) @ ( slbdtrb0 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[8218:[bind(A,$thf( slbdtrb0 @ sk1 ))]]) ).

thf(14127,plain,
    ( ( xO != szNzAzT0 )
    | ( aSubsetOf0 @ ( slbdtrb0 @ sk1 ) @ slcrc0 )
    | ( ( slbdtrb0 @ sk1 )
     != ( slbdtrb0 @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[137,8219]) ).

thf(14220,plain,
    ( ( aSubsetOf0 @ ( slbdtrb0 @ sk1 ) @ slcrc0 )
    | ( xO != szNzAzT0 )
    | ( sk1 != sz00 ) ),
    inference(simp,[status(thm)],[14127]) ).

thf(60,axiom,
    ( ( aSet0 @ szNzAzT0 )
    & ( isCountable0 @ szNzAzT0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

thf(361,plain,
    ( ( aSet0 @ szNzAzT0 )
    & ( isCountable0 @ szNzAzT0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(363,plain,
    aSet0 @ szNzAzT0,
    inference(cnf,[status(esa)],[361]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardS) ).

thf(130,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(131,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
    inference(cnf,[status(esa)],[130]) ).

thf(1368,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ szNzAzT0 )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[363,131]) ).

thf(1369,plain,
    aElement0 @ ( sbrdtbr0 @ szNzAzT0 ),
    inference(pattern_uni,[status(thm)],[1368:[bind(A,$thf( szNzAzT0 ))]]) ).

thf(17,axiom,
    xK != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3520) ).

thf(138,plain,
    xK != sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( C
            = ( sdtpldt0 @ A @ B ) )
        <=> ( ( aSet0 @ C )
            & ! [D: $i] :
                ( ( aElementOf0 @ D @ C )
              <=> ( ( aElement0 @ D )
                  & ( ( aElementOf0 @ D @ A )
                    | ( D = B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).

thf(518,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( ( C
              = ( sdtpldt0 @ A @ B ) )
           => ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElement0 @ D )
                      & ( ( aElementOf0 @ D @ A )
                        | ( D = B ) ) ) )
                  & ( ( ( aElement0 @ D )
                      & ( ( aElementOf0 @ D @ A )
                        | ( D = B ) ) )
                   => ( aElementOf0 @ D @ C ) ) ) ) )
          & ( ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElement0 @ D )
                      & ( ( aElementOf0 @ D @ A )
                        | ( D = B ) ) ) )
                  & ( ( ( aElement0 @ D )
                      & ( ( aElementOf0 @ D @ A )
                        | ( D = B ) ) )
                   => ( aElementOf0 @ D @ C ) ) ) )
           => ( C
              = ( sdtpldt0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(57,axiom,
    aElementOf0 @ xK @ szNzAzT0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).

thf(325,plain,
    aElementOf0 @ xK @ szNzAzT0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(861,plain,
    ! [A: $i] :
      ( ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,517]) ).

thf(862,plain,
    ( ( xK = sz00 )
    | ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[861:[bind(A,$thf( xK ))]]) ).

thf(12,axiom,
    xK != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).

thf(127,plain,
    xK != sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(128,plain,
    xK != sz00,
    inference(polarity_switch,[status(thm)],[127]) ).

thf(129,plain,
    xK != sz00,
    inference(lifteq,[status(thm)],[128]) ).

thf(1560,plain,
    aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0,
    inference(simplifyReflect,[status(thm)],[862,129]) ).

thf(7772,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,186]) ).

thf(7773,plain,
    aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ),
    inference(pattern_uni,[status(thm)],[7772:[bind(A,$thf( sk31 @ xK ))]]) ).

thf(7989,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7773,135]) ).

thf(7990,plain,
    aSubsetOf0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) @ ( slbdtrb0 @ ( sk31 @ xK ) ),
    inference(pattern_uni,[status(thm)],[7989:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xK ) ))]]) ).

thf(362,plain,
    isCountable0 @ szNzAzT0,
    inference(cnf,[status(esa)],[361]) ).

thf(8,axiom,
    isFinite0 @ slcrc0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).

thf(115,plain,
    isFinite0 @ slcrc0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(7769,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,186]) ).

thf(7770,plain,
    aSet0 @ ( slbdtrb0 @ xK ),
    inference(pattern_uni,[status(thm)],[7769:[bind(A,$thf( xK ))]]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isCountable0 @ A ) )
     => ~ ( isFinite0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).

thf(158,plain,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isCountable0 @ A ) )
     => ~ ( isFinite0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(159,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isCountable0 @ A )
      | ~ ( isFinite0 @ A ) ),
    inference(cnf,[status(esa)],[158]) ).

thf(7839,plain,
    ! [A: $i] :
      ( ~ ( isCountable0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ xK ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7770,159]) ).

thf(7840,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
    | ~ ( isFinite0 @ ( slbdtrb0 @ xK ) ) ),
    inference(pattern_uni,[status(thm)],[7839:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).

thf(19626,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
    | ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,7840]) ).

thf(19734,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
    | ( ( slbdtrb0 @ xK )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[19626]) ).

thf(29209,plain,
    ( ( ( slbdtrb0 @ xK )
     != slcrc0 )
    | ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
     != ( isCountable0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[362,19734]) ).

thf(29267,plain,
    ( ( ( slbdtrb0 @ xK )
     != slcrc0 )
    | ( ( slbdtrb0 @ xK )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[29209]) ).

thf(4285,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( isCountable0 @ xS )
       != ( isCountable0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[456,159]) ).

thf(4286,plain,
    ( ~ ( aSet0 @ xS )
    | ~ ( isFinite0 @ xS ) ),
    inference(pattern_uni,[status(thm)],[4285:[bind(A,$thf( xS ))]]) ).

thf(8023,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) )
     != ( aSet0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[7773,4286]) ).

thf(8030,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( slbdtrb0 @ ( sk31 @ xK ) )
     != xS ) ),
    inference(simp,[status(thm)],[8023]) ).

thf(1671,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ szNzAzT0 )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[363,135]) ).

thf(1672,plain,
    aSubsetOf0 @ szNzAzT0 @ szNzAzT0,
    inference(pattern_uni,[status(thm)],[1671:[bind(A,$thf( szNzAzT0 ))]]) ).

thf(29942,plain,
    ! [A: $i] :
      ( ( A = slcrc0 )
      | ( aElementOf0 @ ( szmzizndt0 @ A ) @ A )
      | ( ( aSubsetOf0 @ szNzAzT0 @ szNzAzT0 )
       != ( aSubsetOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1672,250]) ).

thf(29943,plain,
    ( ( szNzAzT0 = slcrc0 )
    | ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[29942:[bind(A,$thf( szNzAzT0 ))]]) ).

thf(652,plain,
    ( ( isCountable0 @ szNzAzT0 )
   != ( isCountable0 @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[362,647]) ).

thf(654,plain,
    szNzAzT0 != slcrc0,
    inference(simp,[status(thm)],[652]) ).

thf(31786,plain,
    aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0,
    inference(simplifyReflect,[status(thm)],[29943,654]) ).

thf(31911,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[31786,186]) ).

thf(31912,plain,
    aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[31911:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).

thf(34099,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) )
     != ( aSet0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[31912,4286]) ).

thf(34103,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) )
     != xS ) ),
    inference(simp,[status(thm)],[34099]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( ( isFinite0 @ A )
            & ( aElementOf0 @ B @ A ) )
         => ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
            = ( sbrdtbr0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).

thf(232,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( ( isFinite0 @ A )
            & ( aElementOf0 @ B @ A ) )
         => ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
            = ( sbrdtbr0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(233,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ~ ( aElementOf0 @ B @ A )
      | ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
        = ( sbrdtbr0 @ A ) ) ),
    inference(cnf,[status(esa)],[232]) ).

thf(234,plain,
    ! [B: $i,A: $i] :
      ( ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
        = ( sbrdtbr0 @ A ) )
      | ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ~ ( aElementOf0 @ B @ A ) ),
    inference(lifteq,[status(thm)],[233]) ).

thf(9572,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7766,131]) ).

thf(9573,plain,
    ( ( xk = sz00 )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[9572:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xk ) ))]]) ).

thf(20055,plain,
    ! [A: $i] :
      ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,218]) ).

thf(20056,plain,
    isCountable0 @ ( sdtlpdtrp0 @ xN @ xK ),
    inference(pattern_uni,[status(thm)],[20055:[bind(A,$thf( xK ))]]) ).

thf(7778,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,186]) ).

thf(7779,plain,
    aSet0 @ ( slbdtrb0 @ xk ),
    inference(pattern_uni,[status(thm)],[7778:[bind(A,$thf( xk ))]]) ).

thf(7913,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ xk ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7779,135]) ).

thf(7914,plain,
    aSubsetOf0 @ ( slbdtrb0 @ xk ) @ ( slbdtrb0 @ xk ),
    inference(pattern_uni,[status(thm)],[7913:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).

thf(9286,plain,
    ( ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ xk ) )
    | ( ( slbdtrb0 @ xk )
     != ( slbdtrb0 @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[137,7914]) ).

thf(9351,plain,
    ( ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ xk ) )
    | ( xk != sz00 ) ),
    inference(simp,[status(thm)],[9286]) ).

thf(29,axiom,
    ( ( aFunction0 @ xe )
    & ( ( szDzozmdt0 @ xe )
      = szNzAzT0 )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ( ( sdtlpdtrp0 @ xe @ A )
          = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).

thf(162,plain,
    ( ( aFunction0 @ xe )
    & ( ( szDzozmdt0 @ xe )
      = szNzAzT0 )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ( ( sdtlpdtrp0 @ xe @ A )
          = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(163,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
    inference(cnf,[status(esa)],[162]) ).

thf(166,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 ) ),
    inference(lifteq,[status(thm)],[163]) ).

thf(4720,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,166]) ).

thf(4721,plain,
    ( ( sdtlpdtrp0 @ xe @ xK )
    = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) ),
    inference(pattern_uni,[status(thm)],[4720:[bind(A,$thf( xK ))]]) ).

thf(20223,plain,
    ( ( isCountable0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) )
    | ( ( sdtlpdtrp0 @ xN @ xK )
     != ( sdtlpdtrp0 @ xe @ xK ) ) ),
    inference(paramod_ordered,[status(thm)],[4721,20056]) ).

thf(20285,plain,
    ( ( isCountable0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) )
    | ( xN != xe )
    | ( xK != xK ) ),
    inference(simp,[status(thm)],[20223]) ).

thf(20310,plain,
    ( ( isCountable0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) )
    | ( xN != xe ) ),
    inference(simp,[status(thm)],[20285]) ).

thf(69577,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
    | ( xN != xe )
    | ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) )
     != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xK ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4721,20310]) ).

thf(69578,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
    | ( xN != xe ) ),
    inference(pattern_uni,[status(thm)],[69577:[]]) ).

thf(69861,plain,
    ( ( xN != xe )
    | ( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
     != ( isCountable0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[69578,647]) ).

thf(69974,plain,
    ( ( xN != xe )
    | ( ( sdtlpdtrp0 @ xe @ xK )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[69861]) ).

thf(9,axiom,
    ( ( aFunction0 @ xc )
    & ( ( szDzozmdt0 @ xc )
      = ( slbdtsldtrb0 @ xS @ xK ) )
    & ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).

thf(116,plain,
    ( ( aFunction0 @ xc )
    & ( ( szDzozmdt0 @ xc )
      = ( slbdtsldtrb0 @ xS @ xK ) )
    & ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(119,plain,
    aFunction0 @ xc,
    inference(cnf,[status(esa)],[116]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).

thf(121,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(122,plain,
    ! [A: $i] :
      ( ~ ( aFunction0 @ A )
      | ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
    inference(cnf,[status(esa)],[121]) ).

thf(1250,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( szDzozmdt0 @ A ) )
      | ( ( aFunction0 @ xc )
       != ( aFunction0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[119,122]) ).

thf(1251,plain,
    aSet0 @ ( szDzozmdt0 @ xc ),
    inference(pattern_uni,[status(thm)],[1250:[bind(A,$thf( xc ))]]) ).

thf(4297,plain,
    ! [A: $i] :
      ( ~ ( isCountable0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1251,159]) ).

thf(4298,plain,
    ( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
    | ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) ) ),
    inference(pattern_uni,[status(thm)],[4297:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).

thf(7325,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
     != ( isCountable0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[362,4298]) ).

thf(7368,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[7325]) ).

thf(118,plain,
    ( ( szDzozmdt0 @ xc )
    = ( slbdtsldtrb0 @ xS @ xK ) ),
    inference(cnf,[status(esa)],[116]) ).

thf(120,plain,
    ( ( slbdtsldtrb0 @ xS @ xK )
    = ( szDzozmdt0 @ xc ) ),
    inference(lifteq,[status(thm)],[118]) ).

thf(507,plain,
    ( ( szszuzczcdt0 @ xk )
    = xK ),
    inference(cnf,[status(esa)],[506]) ).

thf(509,plain,
    ( ( szszuzczcdt0 @ xk )
    = xK ),
    inference(lifteq,[status(thm)],[507]) ).

thf(3357,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( ( szszuzczcdt0 @ sz00 )
      = xK )
    | ( xk != xk ) ),
    inference(paramod_ordered,[status(thm)],[873,509]) ).

thf(3358,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( ( szszuzczcdt0 @ sz00 )
      = xK ) ),
    inference(pattern_uni,[status(thm)],[3357:[]]) ).

thf(7780,plain,
    ! [A: $i] :
      ( ( ( szszuzczcdt0 @ sz00 )
        = xK )
      | ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[3358,186]) ).

thf(7781,plain,
    ( ( ( szszuzczcdt0 @ sz00 )
      = xK )
    | ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ),
    inference(pattern_uni,[status(thm)],[7780:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(33,axiom,
    aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) @ xT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4758) ).

thf(202,plain,
    aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) @ xT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(3381,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[873,517]) ).

thf(3382,plain,
    ( ( xk = sz00 )
    | ( ( sk31 @ xk )
      = sz00 )
    | ( aElementOf0 @ ( sk31 @ ( sk31 @ xk ) ) @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[3381:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(4713,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[873,166]) ).

thf(4714,plain,
    ( ( xk = sz00 )
    | ( ( sdtlpdtrp0 @ xe @ ( sk31 @ xk ) )
      = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4713:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(8212,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ~ ( isCountable0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7814,159]) ).

thf(8213,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
    | ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[8212:[bind(A,$thf( slbdtrb0 @ sk1 ))]]) ).

thf(24422,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,8213]) ).

thf(24557,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( slbdtrb0 @ sk1 )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[24422]) ).

thf(59063,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( slbdtrb0 @ sk1 )
     != ( slbdtrb0 @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[137,24557]) ).

thf(59208,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
    | ( sk1 != sz00 ) ),
    inference(simp,[status(thm)],[59063]) ).

thf(59348,plain,
    ( ( xO != szNzAzT0 )
    | ( sk1 != sz00 )
    | ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
     != ( isCountable0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[362,59208]) ).

thf(59412,plain,
    ( ( xO != szNzAzT0 )
    | ( sk1 != sz00 )
    | ( ( slbdtrb0 @ sk1 )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[59348]) ).

thf(20,axiom,
    ( ( aSet0 @ xT )
    & ( isFinite0 @ xT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).

thf(145,plain,
    ( ( aSet0 @ xT )
    & ( isFinite0 @ xT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(147,plain,
    aSet0 @ xT,
    inference(cnf,[status(esa)],[145]) ).

thf(4295,plain,
    ! [A: $i] :
      ( ~ ( isCountable0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( aSet0 @ xT )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,159]) ).

thf(4296,plain,
    ( ~ ( isCountable0 @ xT )
    | ~ ( isFinite0 @ xT ) ),
    inference(pattern_uni,[status(thm)],[4295:[bind(A,$thf( xT ))]]) ).

thf(146,plain,
    isFinite0 @ xT,
    inference(cnf,[status(esa)],[145]) ).

thf(4359,plain,
    ( ~ ( isCountable0 @ xT )
    | ~ $true ),
    inference(rewrite,[status(thm)],[4296,146]) ).

thf(4360,plain,
    ~ ( isCountable0 @ xT ),
    inference(simp,[status(thm)],[4359]) ).

thf(4362,plain,
    ( ( isCountable0 @ xT )
   != ( isCountable0 @ xS ) ),
    inference(paramod_ordered,[status(thm)],[456,4360]) ).

thf(4376,plain,
    xT != xS,
    inference(simp,[status(thm)],[4362]) ).

thf(217,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 ) ),
    inference(cnf,[status(esa)],[216]) ).

thf(51,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( C
            = ( sdtmndt0 @ A @ B ) )
        <=> ( ( aSet0 @ C )
            & ! [D: $i] :
                ( ( aElementOf0 @ D @ C )
              <=> ( ( aElement0 @ D )
                  & ( aElementOf0 @ D @ A )
                  & ( D != B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

thf(262,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( ( C
              = ( sdtmndt0 @ A @ B ) )
           => ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElement0 @ D )
                      & ( aElementOf0 @ D @ A )
                      & ( D != B ) ) )
                  & ( ( ( aElement0 @ D )
                      & ( aElementOf0 @ D @ A )
                      & ( D != B ) )
                   => ( aElementOf0 @ D @ C ) ) ) ) )
          & ( ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElement0 @ D )
                      & ( aElementOf0 @ D @ A )
                      & ( D != B ) ) )
                  & ( ( ( aElement0 @ D )
                      & ( aElementOf0 @ D @ A )
                      & ( D != B ) )
                   => ( aElementOf0 @ D @ C ) ) ) )
           => ( C
              = ( sdtmndt0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(263,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElement0 @ B ) )
     => ( ! [C: $i] :
            ( ( C
              = ( sdtmndt0 @ A @ B ) )
           => ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( aElementOf0 @ D @ C )
                 => ( ( aElement0 @ D )
                    & ( aElementOf0 @ D @ A )
                    & ( D != B ) ) )
              & ! [D: $i] :
                  ( ( ( aElement0 @ D )
                    & ( aElementOf0 @ D @ A )
                    & ( D != B ) )
                 => ( aElementOf0 @ D @ C ) ) ) )
        & ! [C: $i] :
            ( ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( aElementOf0 @ D @ C )
                 => ( ( aElement0 @ D )
                    & ( aElementOf0 @ D @ A )
                    & ( D != B ) ) )
              & ! [D: $i] :
                  ( ( ( aElement0 @ D )
                    & ( aElementOf0 @ D @ A )
                    & ( D != B ) )
                 => ( aElementOf0 @ D @ C ) ) )
           => ( C
              = ( sdtmndt0 @ A @ B ) ) ) ) ),
    inference(miniscope,[status(thm)],[262]) ).

thf(269,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ( C
       != ( sdtmndt0 @ A @ B ) )
      | ~ ( aElement0 @ D )
      | ~ ( aElementOf0 @ D @ A )
      | ( D = B )
      | ( aElementOf0 @ D @ C ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(275,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtmndt0 @ A @ B ) )
      | ( D = B )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElement0 @ D )
      | ~ ( aElementOf0 @ D @ A )
      | ( aElementOf0 @ D @ C ) ),
    inference(lifteq,[status(thm)],[269]) ).

thf(276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElement0 @ C )
      | ~ ( aElementOf0 @ C @ A )
      | ( aElementOf0 @ C @ ( sdtmndt0 @ A @ B ) ) ),
    inference(simp,[status(thm)],[275]) ).

thf(4710,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,166]) ).

thf(4711,plain,
    ( ( sdtlpdtrp0 @ xe @ xk )
    = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xk ) ) ),
    inference(pattern_uni,[status(thm)],[4710:[bind(A,$thf( xk ))]]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( ( ( sbrdtbr0 @ A )
          = sz00 )
      <=> ( A = slcrc0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).

thf(105,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( ( ( ( sbrdtbr0 @ A )
            = sz00 )
         => ( A = slcrc0 ) )
        & ( ( A = slcrc0 )
         => ( ( sbrdtbr0 @ A )
            = sz00 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(106,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 ) ),
    inference(cnf,[status(esa)],[105]) ).

thf(108,plain,
    ! [A: $i] :
      ( ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 )
      | ~ ( aSet0 @ A ) ),
    inference(lifteq,[status(thm)],[106]) ).

thf(667,plain,
    ! [A: $i] :
      ( ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 )
      | ( ( aSet0 @ szNzAzT0 )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[363,108]) ).

thf(668,plain,
    ( ( ( sbrdtbr0 @ szNzAzT0 )
     != sz00 )
    | ( szNzAzT0 = slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( szNzAzT0 ))]]) ).

thf(3745,plain,
    ( ( sbrdtbr0 @ szNzAzT0 )
   != sz00 ),
    inference(simplifyReflect,[status(thm)],[668,654]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( sdtlseqdt0 @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).

thf(225,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( sdtlseqdt0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(226,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( sdtlseqdt0 @ A @ A ) ),
    inference(cnf,[status(esa)],[225]) ).

thf(22969,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,226]) ).

thf(22970,plain,
    sdtlseqdt0 @ xk @ xk,
    inference(pattern_uni,[status(thm)],[22969:[bind(A,$thf( xk ))]]) ).

thf(31,axiom,
    ( ( aSet0 @ xO )
    & ( isCountable0 @ xO ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).

thf(197,plain,
    ( ( aSet0 @ xO )
    & ( isCountable0 @ xO ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(199,plain,
    aSet0 @ xO,
    inference(cnf,[status(esa)],[197]) ).

thf(1669,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ xO )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[199,135]) ).

thf(1670,plain,
    aSubsetOf0 @ xO @ xO,
    inference(pattern_uni,[status(thm)],[1669:[bind(A,$thf( xO ))]]) ).

thf(368,plain,
    ! [B: $i,A: $i] :
      ( ( A != slcrc0 )
      | ~ ( aElementOf0 @ B @ A ) ),
    inference(cnf,[status(esa)],[365]) ).

thf(373,plain,
    ! [B: $i,A: $i] :
      ( ( A != slcrc0 )
      | ~ ( aElementOf0 @ B @ A ) ),
    inference(lifteq,[status(thm)],[368]) ).

thf(374,plain,
    ! [A: $i] :
      ~ ( aElementOf0 @ A @ slcrc0 ),
    inference(simp,[status(thm)],[373]) ).

thf(605,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ sk1 @ xO )
     != ( aElementOf0 @ A @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[101,374]) ).

thf(606,plain,
    ! [A: $i] :
      ( ( sk1 != A )
      | ( xO != slcrc0 ) ),
    inference(simp,[status(thm)],[605]) ).

thf(607,plain,
    xO != slcrc0,
    inference(simp,[status(thm)],[606]) ).

thf(30910,plain,
    ! [A: $i] :
      ( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ( aElementOf0 @ ( szmzizndt0 @ A ) @ A )
      | ( A != xO ) ),
    inference(paramod_ordered,[status(thm)],[250,607]) ).

thf(30911,plain,
    ( ~ ( aSubsetOf0 @ xO @ szNzAzT0 )
    | ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO ) ),
    inference(pattern_uni,[status(thm)],[30910:[bind(A,$thf( xO ))]]) ).

thf(32016,plain,
    ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
    | ( ( aSubsetOf0 @ xO @ xO )
     != ( aSubsetOf0 @ xO @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1670,30911]) ).

thf(32050,plain,
    ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
    | ( xO != xO )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32016]) ).

thf(32083,plain,
    ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32050]) ).

thf(94,axiom,
    ( ( aFunction0 @ xN )
    & ( ( szDzozmdt0 @ xN )
      = szNzAzT0 )
    & ( ( sdtlpdtrp0 @ xN @ sz00 )
      = xS )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ( ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
            & ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
         => ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
            & ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).

thf(587,plain,
    ( ( aFunction0 @ xN )
    & ( ( szDzozmdt0 @ xN )
      = szNzAzT0 )
    & ( ( sdtlpdtrp0 @ xN @ sz00 )
      = xS )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ( ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
            & ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
         => ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
            & ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(588,plain,
    ( ( sdtlpdtrp0 @ xN @ sz00 )
    = xS ),
    inference(cnf,[status(esa)],[587]) ).

thf(594,plain,
    ( ( sdtlpdtrp0 @ xN @ sz00 )
    = xS ),
    inference(lifteq,[status(thm)],[588]) ).

thf(47,axiom,
    aElementOf0 @ sz00 @ szNzAzT0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).

thf(240,plain,
    aElementOf0 @ sz00 @ szNzAzT0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(100,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
      | ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 ) ),
    inference(cnf,[status(esa)],[99]) ).

thf(102,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
    inference(lifteq,[status(thm)],[100]) ).

thf(672,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
      | ( ( aElementOf0 @ sz00 @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[240,102]) ).

thf(673,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sz00 )
     != sk1 )
    | ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
    inference(pattern_uni,[status(thm)],[672:[bind(A,$thf( sz00 ))]]) ).

thf(785,plain,
    ( ( sk1 != xS )
    | ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
    | ( ( sdtlpdtrp0 @ xN @ sz00 )
     != ( sdtlpdtrp0 @ xe @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[594,673]) ).

thf(790,plain,
    ( ( sk1 != xS )
    | ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
    | ( xN != xe )
    | ( sz00 != sz00 ) ),
    inference(simp,[status(thm)],[785]) ).

thf(797,plain,
    ( ( sk1 != xS )
    | ~ ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
    | ( xN != xe ) ),
    inference(simp,[status(thm)],[790]) ).

thf(715,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,102]) ).

thf(716,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xk )
     != sk1 )
    | ~ ( aElementOf0 @ xk @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
    inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( xk ))]]) ).

thf(804,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xk )
     != sk1 )
    | ( ( aElementOf0 @ xk @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
     != ( aElementOf0 @ xk @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,716]) ).

thf(811,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xk )
     != sk1 )
    | ( xk != xk )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[804]) ).

thf(814,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xk )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[811]) ).

thf(24448,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,8213]) ).

thf(24560,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( slbdtrb0 @ sk1 )
     != xS ) ),
    inference(simp,[status(thm)],[24448]) ).

thf(4754,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
      | ( ( aElementOf0 @ sz00 @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[240,166]) ).

thf(4755,plain,
    ( ( sdtlpdtrp0 @ xe @ sz00 )
    = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ sz00 ) ) ),
    inference(pattern_uni,[status(thm)],[4754:[bind(A,$thf( sz00 ))]]) ).

thf(5090,plain,
    ( ( sdtlpdtrp0 @ xe @ sz00 )
    = ( szmzizndt0 @ xS ) ),
    inference(rewrite,[status(thm)],[4755,594]) ).

thf(5112,plain,
    ( ( ( szmzizndt0 @ xS )
      = xS )
    | ( ( sdtlpdtrp0 @ xN @ sz00 )
     != ( sdtlpdtrp0 @ xe @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[594,5090]) ).

thf(5144,plain,
    ( ( ( szmzizndt0 @ xS )
      = xS )
    | ( xN != xe )
    | ( sz00 != sz00 ) ),
    inference(simp,[status(thm)],[5112]) ).

thf(5164,plain,
    ( ( ( szmzizndt0 @ xS )
      = xS )
    | ( xN != xe ) ),
    inference(simp,[status(thm)],[5144]) ).

thf(32003,plain,
    ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
    | ( ( aSubsetOf0 @ xS @ szNzAzT0 )
     != ( aSubsetOf0 @ xO @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[457,30911]) ).

thf(32058,plain,
    ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
    | ( xS != xO )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32003]) ).

thf(32088,plain,
    ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
    | ( xS != xO ) ),
    inference(simp,[status(thm)],[32058]) ).

thf(35062,plain,
    ( ( xN != xe )
    | ( aElementOf0 @ xS @ xO )
    | ( xS != xO )
    | ( ( szmzizndt0 @ xS )
     != ( szmzizndt0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[5164,32088]) ).

thf(35088,plain,
    ( ( aElementOf0 @ xS @ xO )
    | ( xN != xe )
    | ( xS != xO )
    | ( xS != xO ) ),
    inference(simp,[status(thm)],[35062]) ).

thf(35134,plain,
    ( ( aElementOf0 @ xS @ xO )
    | ( xN != xe )
    | ( xS != xO ) ),
    inference(simp,[status(thm)],[35088]) ).

thf(7872,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ xK ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7770,131]) ).

thf(7873,plain,
    aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ xK ) ),
    inference(pattern_uni,[status(thm)],[7872:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).

thf(35,axiom,
    ( ( aFunction0 @ xd )
    & ( ( szDzozmdt0 @ xd )
      = szNzAzT0 )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ! [B: $i] :
            ( ( ( aSet0 @ B )
              & ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
           => ( ( sdtlpdtrp0 @ xd @ A )
              = ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).

thf(204,plain,
    ( ( aFunction0 @ xd )
    & ( ( szDzozmdt0 @ xd )
      = szNzAzT0 )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ! [B: $i] :
            ( ( ( aSet0 @ B )
              & ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
           => ( ( sdtlpdtrp0 @ xd @ A )
              = ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(206,plain,
    ( ( szDzozmdt0 @ xd )
    = szNzAzT0 ),
    inference(cnf,[status(esa)],[204]) ).

thf(209,plain,
    ( ( szDzozmdt0 @ xd )
    = szNzAzT0 ),
    inference(lifteq,[status(thm)],[206]) ).

thf(12816,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xd ) ) ),
    inference(paramod_ordered,[status(thm)],[209,7368]) ).

thf(12864,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( xc != xd ) ),
    inference(simp,[status(thm)],[12816]) ).

thf(12874,plain,
    ( ( xc != xd )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,12864]) ).

thf(12921,plain,
    ( ( xc != xd )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[12874]) ).

thf(589,plain,
    ( ( szDzozmdt0 @ xN )
    = szNzAzT0 ),
    inference(cnf,[status(esa)],[587]) ).

thf(593,plain,
    ( ( szDzozmdt0 @ xN )
    = szNzAzT0 ),
    inference(lifteq,[status(thm)],[589]) ).

thf(12800,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xN )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[593,7368]) ).

thf(12865,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( xN != xc ) ),
    inference(simp,[status(thm)],[12800]) ).

thf(850,plain,
    ! [A: $i] :
      ( ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[101,517]) ).

thf(1165,plain,
    ! [A: $i] :
      ( ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( sk1 != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[850]) ).

thf(1175,plain,
    ( ( sk1 = sz00 )
    | ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[1165]) ).

thf(1181,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( xO != szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[1175,101]) ).

thf(1182,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( xO != szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO ) ),
    inference(pattern_uni,[status(thm)],[1181:[]]) ).

thf(1343,plain,
    ( ( xO != szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
     != ( aElementOf0 @ sz00 @ xO ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[1182]) ).

thf(1346,plain,
    ( ( aElementOf0 @ sz00 @ xO )
    | ( xO != szNzAzT0 )
    | ( ( sk31 @ sk1 )
     != sz00 )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[1343]) ).

thf(1354,plain,
    ( ( aElementOf0 @ sz00 @ xO )
    | ( xO != szNzAzT0 )
    | ( ( sk31 @ sk1 )
     != sz00 ) ),
    inference(simp,[status(thm)],[1346]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isFinite0 @ B ) )
         => ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).

thf(152,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isFinite0 @ B ) )
         => ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(153,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElement0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( isFinite0 @ B )
      | ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[152]) ).

thf(75,axiom,
    ( ( aFunction0 @ xC )
    & ( ( szDzozmdt0 @ xC )
      = szNzAzT0 )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ( ( aFunction0 @ ( sdtlpdtrp0 @ xC @ A ) )
          & ( ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) )
            = ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) )
          & ! [B: $i] :
              ( ( ( aSet0 @ B )
                & ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
             => ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
                = ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).

thf(446,plain,
    ( ( aFunction0 @ xC )
    & ( ( szDzozmdt0 @ xC )
      = szNzAzT0 )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ( ( aFunction0 @ ( sdtlpdtrp0 @ xC @ A ) )
          & ( ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) )
            = ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) )
          & ! [B: $i] :
              ( ( ( aSet0 @ B )
                & ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
             => ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
                = ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(447,plain,
    ( ( szDzozmdt0 @ xC )
    = szNzAzT0 ),
    inference(cnf,[status(esa)],[446]) ).

thf(454,plain,
    ( ( szDzozmdt0 @ xC )
    = szNzAzT0 ),
    inference(lifteq,[status(thm)],[447]) ).

thf(1667,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1251,135]) ).

thf(1668,plain,
    aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ ( szDzozmdt0 @ xc ),
    inference(pattern_uni,[status(thm)],[1667:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).

thf(1740,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xC )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[454,1668]) ).

thf(1746,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( xC != xc ) ),
    inference(simp,[status(thm)],[1740]) ).

thf(34038,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[31912,135]) ).

thf(34039,plain,
    aSubsetOf0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[34038:[bind(A,$thf( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ))]]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ? [B: $i] :
          ( ( aElementOf0 @ B @ xT )
          & ! [C: $i] :
              ( ( ( aSet0 @ C )
                & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
             => ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
                = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4618) ).

thf(258,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ? [B: $i] :
          ( ( aElementOf0 @ B @ xT )
          & ! [C: $i] :
              ( ( ( aSet0 @ C )
                & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) )
             => ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
                = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(259,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( aElementOf0 @ ( sk7 @ A ) @ xT ) ),
    inference(cnf,[status(esa)],[258]) ).

thf(39683,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,259]) ).

thf(39684,plain,
    aElementOf0 @ ( sk7 @ xk ) @ xT,
    inference(pattern_uni,[status(thm)],[39683:[bind(A,$thf( xk ))]]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ A )
         => ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
            = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).

thf(237,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ A )
         => ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(238,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElementOf0 @ B @ A )
      | ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
        = A ) ),
    inference(cnf,[status(esa)],[237]) ).

thf(239,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
        = A )
      | ~ ( aSet0 @ A )
      | ~ ( aElementOf0 @ B @ A ) ),
    inference(lifteq,[status(thm)],[238]) ).

thf(26090,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
        = A )
      | ~ ( aSet0 @ A )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[101,239]) ).

thf(26091,plain,
    ( ( ( sdtpldt0 @ ( sdtmndt0 @ xO @ sk1 ) @ sk1 )
      = xO )
    | ~ ( aSet0 @ xO ) ),
    inference(pattern_uni,[status(thm)],[26090:[bind(A,$thf( xO )),bind(B,$thf( sk1 ))]]) ).

thf(68751,plain,
    ( ( ( sdtpldt0 @ ( sdtmndt0 @ xO @ sk1 ) @ sk1 )
      = xO )
    | ~ $true ),
    inference(rewrite,[status(thm)],[26091,199]) ).

thf(68752,plain,
    ( ( sdtpldt0 @ ( sdtmndt0 @ xO @ sk1 ) @ sk1 )
    = xO ),
    inference(simp,[status(thm)],[68751]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
        & ( ( szszuzczcdt0 @ A )
         != sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).

thf(417,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
        & ( ( szszuzczcdt0 @ A )
         != sz00 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ( C
       != ( sdtmndt0 @ A @ B ) )
      | ~ ( aElementOf0 @ D @ C )
      | ( aElementOf0 @ D @ A ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(287,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElementOf0 @ D @ C )
      | ( aElementOf0 @ D @ A ) ),
    inference(lifteq,[status(thm)],[272]) ).

thf(288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElementOf0 @ C @ ( sdtmndt0 @ A @ B ) )
      | ( aElementOf0 @ C @ A ) ),
    inference(simp,[status(thm)],[287]) ).

thf(19068,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[873,217]) ).

thf(19069,plain,
    ( ( xk = sz00 )
    | ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[19068:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(1264,plain,
    ! [A: $i] :
      ( ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 )
      | ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1251,108]) ).

thf(1265,plain,
    ( ( ( sbrdtbr0 @ ( szDzozmdt0 @ xc ) )
     != sz00 )
    | ( ( szDzozmdt0 @ xc )
      = slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[1264:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).

thf(32209,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[32083,186]) ).

thf(32261,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( xO != szNzAzT0 )
      | ( ( szmzizndt0 @ xO )
       != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32209]) ).

thf(32270,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ xO ) ) )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32261]) ).

thf(49,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 )
        & ( A != B ) )
     => ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
       != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).

thf(255,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 )
        & ( A != B ) )
     => ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
       != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(256,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ( A = B )
      | ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
       != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
    inference(cnf,[status(esa)],[255]) ).

thf(257,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
       != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ szNzAzT0 ) ),
    inference(lifteq,[status(thm)],[256]) ).

thf(55,axiom,
    ( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
    & ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).

thf(319,plain,
    ( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
    & ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(320,plain,
    isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ),
    inference(cnf,[status(esa)],[319]) ).

thf(8024,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7773,131]) ).

thf(8025,plain,
    aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( sk31 @ xK ) ) ),
    inference(pattern_uni,[status(thm)],[8024:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xK ) ))]]) ).

thf(173,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ~ ( aElementOf0 @ ( sk3 @ B @ A ) @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk3 @ B @ A ) ) @ A )
      | ~ ( sk2 @ A @ B )
      | ( B
        = ( slbdtrb0 @ A ) ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(183,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ~ ( aElementOf0 @ ( sk3 @ B @ A ) @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk3 @ B @ A ) ) @ A )
      | ~ ( sk2 @ A @ B ) ),
    inference(lifteq,[status(thm)],[173]) ).

thf(184,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ~ ( aElementOf0 @ ( sk3 @ B @ A ) @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk3 @ B @ A ) ) @ A )
      | ~ ( sk2 @ A @ B ) ),
    inference(simp,[status(thm)],[183]) ).

thf(20058,plain,
    ! [A: $i] :
      ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,218]) ).

thf(20059,plain,
    isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ),
    inference(pattern_uni,[status(thm)],[20058:[bind(A,$thf( sk31 @ xK ))]]) ).

thf(4335,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ xS )
     != ( aSet0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[363,4286]) ).

thf(4349,plain,
    ( ~ ( isFinite0 @ xS )
    | ( xS != szNzAzT0 ) ),
    inference(simp,[status(thm)],[4335]) ).

thf(24541,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,8213]) ).

thf(24558,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( slbdtrb0 @ sk1 )
     != xT ) ),
    inference(simp,[status(thm)],[24541]) ).

thf(178,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( B
       != ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ C @ B )
      | ( aElementOf0 @ C @ szNzAzT0 ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ C @ B )
      | ( aElementOf0 @ C @ szNzAzT0 ) ),
    inference(lifteq,[status(thm)],[178]) ).

thf(196,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ ( slbdtrb0 @ A ) )
      | ( aElementOf0 @ B @ szNzAzT0 ) ),
    inference(simp,[status(thm)],[195]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isCountable0 @ B ) )
         => ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCDiffSet) ).

thf(156,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isCountable0 @ B ) )
         => ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElement0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( isCountable0 @ B )
      | ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[156]) ).

thf(32193,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[32083,218]) ).

thf(32225,plain,
    ! [A: $i] :
      ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( xO != szNzAzT0 )
      | ( ( szmzizndt0 @ xO )
       != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32193]) ).

thf(32288,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) ) )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32225]) ).

thf(38229,plain,
    ( ( xO != szNzAzT0 )
    | ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) ) )
     != ( isCountable0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[32288,4360]) ).

thf(38320,plain,
    ( ( xO != szNzAzT0 )
    | ( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) )
     != xT ) ),
    inference(simp,[status(thm)],[38229]) ).

thf(7941,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ ( slbdtrb0 @ xk ) )
     != ( aSet0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[7779,4286]) ).

thf(7945,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( slbdtrb0 @ xk )
     != xS ) ),
    inference(simp,[status(thm)],[7941]) ).

thf(7307,plain,
    ( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,4298]) ).

thf(7372,plain,
    ( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[7307]) ).

thf(18243,plain,
    ( ( ( szDzozmdt0 @ xc )
     != slcrc0 )
    | ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,7372]) ).

thf(18333,plain,
    ( ( ( szDzozmdt0 @ xc )
     != slcrc0 )
    | ( ( szDzozmdt0 @ xc )
     != xS ) ),
    inference(simp,[status(thm)],[18243]) ).

thf(264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ( C
       != ( sdtmndt0 @ A @ B ) )
      | ~ ( aElementOf0 @ D @ C )
      | ( D != B ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(283,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtmndt0 @ A @ B ) )
      | ( D != B )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElementOf0 @ D @ C ) ),
    inference(lifteq,[status(thm)],[264]) ).

thf(284,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElementOf0 @ B @ ( sdtmndt0 @ A @ B ) ) ),
    inference(simp,[status(thm)],[283]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).

thf(227,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(228,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ),
    inference(cnf,[status(esa)],[227]) ).

thf(54,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( sdtlseqdt0 @ A @ B )
      <=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).

thf(316,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
         => ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) ) )
        & ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) )
         => ( sdtlseqdt0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(260,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) )
      | ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
        = ( sk7 @ A ) ) ),
    inference(cnf,[status(esa)],[258]) ).

thf(261,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
        = ( sk7 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ),
    inference(lifteq,[status(thm)],[260]) ).

thf(1358,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ slcrc0 )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[372,131]) ).

thf(1359,plain,
    aElement0 @ ( sbrdtbr0 @ slcrc0 ),
    inference(pattern_uni,[status(thm)],[1358:[bind(A,$thf( slcrc0 ))]]) ).

thf(107,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ( A != slcrc0 )
      | ( ( sbrdtbr0 @ A )
        = sz00 ) ),
    inference(cnf,[status(esa)],[105]) ).

thf(109,plain,
    ! [A: $i] :
      ( ( A != slcrc0 )
      | ( ( sbrdtbr0 @ A )
        = sz00 )
      | ~ ( aSet0 @ A ) ),
    inference(lifteq,[status(thm)],[107]) ).

thf(110,plain,
    ( ( ( sbrdtbr0 @ slcrc0 )
      = sz00 )
    | ~ ( aSet0 @ slcrc0 ) ),
    inference(simp,[status(thm)],[109]) ).

thf(690,plain,
    ( ( ( sbrdtbr0 @ slcrc0 )
      = sz00 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[110,372]) ).

thf(691,plain,
    ( ( sbrdtbr0 @ slcrc0 )
    = sz00 ),
    inference(simp,[status(thm)],[690]) ).

thf(1379,plain,
    aElement0 @ sz00,
    inference(rewrite,[status(thm)],[1359,691]) ).

thf(39710,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ sz00 @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[240,259]) ).

thf(39711,plain,
    aElementOf0 @ ( sk7 @ sz00 ) @ xT,
    inference(pattern_uni,[status(thm)],[39710:[bind(A,$thf( sz00 ))]]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
         => ( aElementOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ ( slbdtsldtrb0 @ xS @ xK ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3965) ).

thf(421,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) )
         => ( aElementOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ ( slbdtsldtrb0 @ xS @ xK ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(20692,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) )
   != ( isCountable0 @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[20059,647]) ).

thf(20772,plain,
    ( ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) )
   != slcrc0 ),
    inference(simp,[status(thm)],[20692]) ).

thf(20842,plain,
    ( ( xO != szNzAzT0 )
    | ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ sk1 ) )
     != ( isCountable0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[20194,4360]) ).

thf(20890,plain,
    ( ( xO != szNzAzT0 )
    | ( ( sdtlpdtrp0 @ xN @ sk1 )
     != xT ) ),
    inference(simp,[status(thm)],[20842]) ).

thf(7785,plain,
    ! [A: $i] :
      ( ( sk1 = sz00 )
      | ( xO != szNzAzT0 )
      | ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1175,186]) ).

thf(7786,plain,
    ( ( sk1 = sz00 )
    | ( xO != szNzAzT0 )
    | ( aSet0 @ ( slbdtrb0 @ ( sk31 @ sk1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7785:[bind(A,$thf( sk31 @ sk1 ))]]) ).

thf(1663,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ xT )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,135]) ).

thf(1664,plain,
    aSubsetOf0 @ xT @ xT,
    inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( xT ))]]) ).

thf(38203,plain,
    ( ( xO != szNzAzT0 )
    | ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) ) )
     != ( isCountable0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[32288,647]) ).

thf(38307,plain,
    ( ( xO != szNzAzT0 )
    | ( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ xO ) )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[38203]) ).

thf(591,plain,
    aFunction0 @ xN,
    inference(cnf,[status(esa)],[587]) ).

thf(321,plain,
    aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT,
    inference(cnf,[status(esa)],[319]) ).

thf(7306,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,4298]) ).

thf(7376,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != xS ) ),
    inference(simp,[status(thm)],[7306]) ).

thf(91,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) )
      <=> ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegSucc) ).

thf(574,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) )
         => ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
            | ( A = B ) ) )
        & ( ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
            | ( A = B ) )
         => ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(19112,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,217]) ).

thf(19113,plain,
    aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ xk ) @ szNzAzT0,
    inference(pattern_uni,[status(thm)],[19112:[bind(A,$thf( xk ))]]) ).

thf(7356,plain,
    ( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,4298]) ).

thf(7374,plain,
    ( ~ ( isCountable0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != xT ) ),
    inference(simp,[status(thm)],[7356]) ).

thf(18706,plain,
    ( ( ( szDzozmdt0 @ xc )
     != xT )
    | ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,7374]) ).

thf(18786,plain,
    ( ( ( szDzozmdt0 @ xc )
     != xT )
    | ( ( szDzozmdt0 @ xc )
     != xS ) ),
    inference(simp,[status(thm)],[18706]) ).

thf(164,plain,
    ( ( szDzozmdt0 @ xe )
    = szNzAzT0 ),
    inference(cnf,[status(esa)],[162]) ).

thf(167,plain,
    ( ( szDzozmdt0 @ xe )
    = szNzAzT0 ),
    inference(lifteq,[status(thm)],[164]) ).

thf(117,plain,
    aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT,
    inference(cnf,[status(esa)],[116]) ).

thf(817,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xe ) ) ),
    inference(paramod_ordered,[status(thm)],[167,117]) ).

thf(821,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( xc != xe ) ),
    inference(simp,[status(thm)],[817]) ).

thf(97,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( sdtlseqdt0 @ A @ B )
       => $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).

thf(602,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ( ( sk10 @ C @ B @ A )
       != B )
      | ( C
        = ( sdtmndt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk10 @ C @ B @ A )
       != B )
      | ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C ) ),
    inference(lifteq,[status(thm)],[270]) ).

thf(280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk10 @ C @ B @ A )
       != B )
      | ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C ) ),
    inference(simp,[status(thm)],[279]) ).

thf(40,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( isFinite0 @ A )
          & ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) )
       => ? [C: $i] :
            ( ( aSubsetOf0 @ C @ A )
            & ( ( sbrdtbr0 @ C )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSubEx) ).

thf(221,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( isFinite0 @ A )
          & ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) )
       => ? [C: $i] :
            ( ( aSubsetOf0 @ C @ A )
            & ( ( sbrdtbr0 @ C )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(198,plain,
    isCountable0 @ xO,
    inference(cnf,[status(esa)],[197]) ).

thf(19681,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
     != ( isCountable0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[198,7840]) ).

thf(19733,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
    | ( ( slbdtrb0 @ xK )
     != xO ) ),
    inference(simp,[status(thm)],[19681]) ).

thf(29008,plain,
    ( ( ( slbdtrb0 @ xK )
     != xO )
    | ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,19733]) ).

thf(29118,plain,
    ( ( ( slbdtrb0 @ xK )
     != xO )
    | ( ( slbdtrb0 @ xK )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[29008]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( ( isFinite0 @ A )
            & ( aSubsetOf0 @ B @ A ) )
         => ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSub) ).

thf(132,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( ( isFinite0 @ A )
            & ( aSubsetOf0 @ B @ A ) )
         => ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(7909,plain,
    ! [A: $i] :
      ( ~ ( isCountable0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ xk ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7779,159]) ).

thf(7910,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
    | ~ ( isFinite0 @ ( slbdtrb0 @ xk ) ) ),
    inference(pattern_uni,[status(thm)],[7909:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).

thf(19768,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
    | ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,7910]) ).

thf(19879,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
    | ( ( slbdtrb0 @ xk )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[19768]) ).

thf(42270,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
    | ( ( slbdtrb0 @ xk )
     != ( slbdtrb0 @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[137,19879]) ).

thf(42399,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
    | ( xk != sz00 ) ),
    inference(simp,[status(thm)],[42270]) ).

thf(69,axiom,
    ( ( aSet0 @ xO )
    & ( xO
      = ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).

thf(425,plain,
    ( ( aSet0 @ xO )
    & ( xO
      = ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(426,plain,
    ( xO
    = ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
    inference(cnf,[status(esa)],[425]) ).

thf(428,plain,
    ( ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
    = xO ),
    inference(lifteq,[status(thm)],[426]) ).

thf(133,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ~ ( aSubsetOf0 @ B @ A )
      | ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ),
    inference(cnf,[status(esa)],[132]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ! [C: $i] :
              ( ( C
                = ( sdtexdt0 @ A @ B ) )
            <=> ( ( aFunction0 @ C )
                & ( ( szDzozmdt0 @ C )
                  = B )
                & ! [D: $i] :
                    ( ( aElementOf0 @ D @ B )
                   => ( ( sdtlpdtrp0 @ C @ D )
                      = ( sdtlpdtrp0 @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefRst) ).

thf(297,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ! [C: $i] :
              ( ( ( C
                  = ( sdtexdt0 @ A @ B ) )
               => ( ( aFunction0 @ C )
                  & ( ( szDzozmdt0 @ C )
                    = B )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ B )
                     => ( ( sdtlpdtrp0 @ C @ D )
                        = ( sdtlpdtrp0 @ A @ D ) ) ) ) )
              & ( ( ( aFunction0 @ C )
                  & ( ( szDzozmdt0 @ C )
                    = B )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ B )
                     => ( ( sdtlpdtrp0 @ C @ D )
                        = ( sdtlpdtrp0 @ A @ D ) ) ) )
               => ( C
                  = ( sdtexdt0 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(298,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ( ! [C: $i] :
                ( ( C
                  = ( sdtexdt0 @ A @ B ) )
               => ( ( aFunction0 @ C )
                  & ( ( szDzozmdt0 @ C )
                    = B )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ B )
                     => ( ( sdtlpdtrp0 @ C @ D )
                        = ( sdtlpdtrp0 @ A @ D ) ) ) ) )
            & ! [C: $i] :
                ( ( ( aFunction0 @ C )
                  & ( ( szDzozmdt0 @ C )
                    = B )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ B )
                     => ( ( sdtlpdtrp0 @ C @ D )
                        = ( sdtlpdtrp0 @ A @ D ) ) ) )
               => ( C
                  = ( sdtexdt0 @ A @ B ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[297]) ).

thf(302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ~ ( aFunction0 @ C )
      | ( ( szDzozmdt0 @ C )
       != B )
      | ( ( sdtlpdtrp0 @ C @ ( sk11 @ C @ B @ A ) )
       != ( sdtlpdtrp0 @ A @ ( sk11 @ C @ B @ A ) ) )
      | ( C
        = ( sdtexdt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[298]) ).

thf(306,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( szDzozmdt0 @ C )
       != B )
      | ( ( sdtlpdtrp0 @ C @ ( sk11 @ C @ B @ A ) )
       != ( sdtlpdtrp0 @ A @ ( sk11 @ C @ B @ A ) ) )
      | ( C
        = ( sdtexdt0 @ A @ B ) )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ~ ( aFunction0 @ C ) ),
    inference(lifteq,[status(thm)],[302]) ).

thf(307,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtlpdtrp0 @ B @ ( sk11 @ B @ ( szDzozmdt0 @ B ) @ A ) )
       != ( sdtlpdtrp0 @ A @ ( sk11 @ B @ ( szDzozmdt0 @ B ) @ A ) ) )
      | ( ( sdtexdt0 @ A @ ( szDzozmdt0 @ B ) )
        = B )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ ( szDzozmdt0 @ B ) @ ( szDzozmdt0 @ A ) )
      | ~ ( aFunction0 @ B ) ),
    inference(simp,[status(thm)],[306]) ).

thf(268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ A )
      | ( C
        = ( sdtmndt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[268]) ).

thf(292,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[291]) ).

thf(243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ( A = slcrc0 )
      | ( B
       != ( szmzizndt0 @ A ) )
      | ~ ( aElementOf0 @ C @ A )
      | ( sdtlseqdt0 @ B @ C ) ),
    inference(cnf,[status(esa)],[242]) ).

thf(247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = slcrc0 )
      | ( B
       != ( szmzizndt0 @ A ) )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ C @ A )
      | ( sdtlseqdt0 @ B @ C ) ),
    inference(lifteq,[status(thm)],[243]) ).

thf(248,plain,
    ! [B: $i,A: $i] :
      ( ( A = slcrc0 )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ A )
      | ( sdtlseqdt0 @ ( szmzizndt0 @ A ) @ B ) ),
    inference(simp,[status(thm)],[247]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).

thf(439,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(20083,plain,
    ! [A: $i] :
      ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ xk @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,218]) ).

thf(20084,plain,
    isCountable0 @ ( sdtlpdtrp0 @ xN @ xk ),
    inference(pattern_uni,[status(thm)],[20083:[bind(A,$thf( xk ))]]) ).

thf(39649,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,259]) ).

thf(39650,plain,
    aElementOf0 @ ( sk7 @ ( sk31 @ xK ) ) @ xT,
    inference(pattern_uni,[status(thm)],[39649:[bind(A,$thf( sk31 @ xK ))]]) ).

thf(59307,plain,
    ( ( xO != szNzAzT0 )
    | ( sk1 != sz00 )
    | ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,59208]) ).

thf(59415,plain,
    ( ( xO != szNzAzT0 )
    | ( sk1 != sz00 )
    | ( ( slbdtrb0 @ sk1 )
     != xS ) ),
    inference(simp,[status(thm)],[59307]) ).

thf(12914,plain,
    ( ( xc != xd )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,12864]) ).

thf(12927,plain,
    ( ( xc != xd )
    | ( ( szDzozmdt0 @ xc )
     != xT ) ),
    inference(simp,[status(thm)],[12914]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ szNzAzT0 )
         => ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelFSet) ).

thf(219,plain,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ szNzAzT0 )
         => ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(220,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[219]) ).

thf(686,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sz00 )
     != sk1 )
    | ( ( aElementOf0 @ sz00 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
     != ( aElementOf0 @ sz00 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[240,673]) ).

thf(688,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sz00 )
     != sk1 )
    | ( sz00 != sz00 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[686]) ).

thf(689,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sz00 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[688]) ).

thf(783,plain,
    ( ( sk1 != xS )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 )
    | ( ( sdtlpdtrp0 @ xN @ sz00 )
     != ( sdtlpdtrp0 @ xe @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[594,689]) ).

thf(792,plain,
    ( ( sk1 != xS )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 )
    | ( xN != xe )
    | ( sz00 != sz00 ) ),
    inference(simp,[status(thm)],[783]) ).

thf(798,plain,
    ( ( sk1 != xS )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 )
    | ( xN != xe ) ),
    inference(simp,[status(thm)],[792]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aFunction0 @ A )
        & ( aElement0 @ B ) )
     => ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).

thf(200,plain,
    ! [A: $i,B: $i] :
      ( ( ( aFunction0 @ A )
        & ( aElement0 @ B ) )
     => ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(201,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aElement0 @ B )
      | ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
    inference(cnf,[status(esa)],[200]) ).

thf(13096,plain,
    ( ( xN != xc )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,12865]) ).

thf(13104,plain,
    ( ( xN != xc )
    | ( ( szDzozmdt0 @ xc )
     != xT ) ),
    inference(simp,[status(thm)],[13096]) ).

thf(4301,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( isCountable0 @ szNzAzT0 )
       != ( isCountable0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[362,159]) ).

thf(4302,plain,
    ( ~ ( aSet0 @ szNzAzT0 )
    | ~ ( isFinite0 @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[4301:[bind(A,$thf( szNzAzT0 ))]]) ).

thf(4556,plain,
    ( ~ $true
    | ~ ( isFinite0 @ szNzAzT0 ) ),
    inference(rewrite,[status(thm)],[4302,363]) ).

thf(4557,plain,
    ~ ( isFinite0 @ szNzAzT0 ),
    inference(simp,[status(thm)],[4556]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ( ( ( aSubsetOf0 @ A @ B )
          & ( aSubsetOf0 @ B @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).

thf(141,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ( ( ( aSubsetOf0 @ A @ B )
          & ( aSubsetOf0 @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(142,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( aSubsetOf0 @ A @ B )
      | ~ ( aSubsetOf0 @ B @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[141]) ).

thf(143,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( aSet0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( aSubsetOf0 @ A @ B )
      | ~ ( aSubsetOf0 @ B @ A ) ),
    inference(lifteq,[status(thm)],[142]) ).

thf(2895,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( aSubsetOf0 @ A @ B )
      | ~ ( aSubsetOf0 @ B @ A )
      | ( B != slcrc0 )
      | ( A != xO ) ),
    inference(paramod_ordered,[status(thm)],[143,607]) ).

thf(2896,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ xO )
      | ~ ( aSet0 @ A )
      | ~ ( aSubsetOf0 @ xO @ A )
      | ~ ( aSubsetOf0 @ A @ xO )
      | ( A != slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[2895:[bind(A,$thf( xO ))]]) ).

thf(3192,plain,
    ( ~ ( aSet0 @ xO )
    | ~ ( aSet0 @ slcrc0 )
    | ~ ( aSubsetOf0 @ xO @ slcrc0 )
    | ~ ( aSubsetOf0 @ slcrc0 @ xO ) ),
    inference(simp,[status(thm)],[2896]) ).

thf(4144,plain,
    ( ~ $true
    | ~ $true
    | ~ ( aSubsetOf0 @ xO @ slcrc0 )
    | ~ ( aSubsetOf0 @ slcrc0 @ xO ) ),
    inference(rewrite,[status(thm)],[3192,372,199]) ).

thf(4145,plain,
    ( ~ ( aSubsetOf0 @ xO @ slcrc0 )
    | ~ ( aSubsetOf0 @ slcrc0 @ xO ) ),
    inference(simp,[status(thm)],[4144]) ).

thf(4152,plain,
    ( ~ ( aSubsetOf0 @ slcrc0 @ xO )
    | ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ ( szDzozmdt0 @ xc ) )
     != ( aSubsetOf0 @ xO @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1668,4145]) ).

thf(4192,plain,
    ( ~ ( aSubsetOf0 @ slcrc0 @ xO )
    | ( ( szDzozmdt0 @ xc )
     != xO )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[4152]) ).

thf(7615,plain,
    ( ( ( szDzozmdt0 @ xc )
     != xO )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 )
    | ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ ( szDzozmdt0 @ xc ) )
     != ( aSubsetOf0 @ slcrc0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[1668,4192]) ).

thf(7677,plain,
    ( ( ( szDzozmdt0 @ xc )
     != xO )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 )
    | ( ( szDzozmdt0 @ xc )
     != xO ) ),
    inference(simp,[status(thm)],[7615]) ).

thf(7703,plain,
    ( ( ( szDzozmdt0 @ xc )
     != xO )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[7677]) ).

thf(34836,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( szmzizndt0 @ xS ) @ xS )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[34726,186]) ).

thf(34853,plain,
    ! [A: $i] :
      ( ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( szmzizndt0 @ xS )
       != A )
      | ( xS != szNzAzT0 ) ),
    inference(simp,[status(thm)],[34836]) ).

thf(34898,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ xS ) ) )
    | ( xS != szNzAzT0 ) ),
    inference(simp,[status(thm)],[34853]) ).

thf(4365,plain,
    ( ( isCountable0 @ xT )
   != ( isCountable0 @ szNzAzT0 ) ),
    inference(paramod_ordered,[status(thm)],[362,4360]) ).

thf(4375,plain,
    xT != szNzAzT0,
    inference(simp,[status(thm)],[4365]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( sdtlseqdt0 @ A @ B )
        | ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).

thf(160,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( sdtlseqdt0 @ A @ B )
        | ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( B
       != ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ C @ B )
      | ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ C @ B )
      | ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ),
    inference(lifteq,[status(thm)],[175]) ).

thf(192,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ ( slbdtrb0 @ A ) )
      | ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ),
    inference(simp,[status(thm)],[191]) ).

thf(70,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( szszuzczcdt0 @ A )
          = ( szszuzczcdt0 @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).

thf(429,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( szszuzczcdt0 @ A )
          = ( szszuzczcdt0 @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(165,plain,
    aFunction0 @ xe,
    inference(cnf,[status(esa)],[162]) ).

thf(609,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[101,102]) ).

thf(611,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( sk1 != A )
      | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
       != xO ) ),
    inference(simp,[status(thm)],[609]) ).

thf(613,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ~ ( aElementOf0 @ sk1 @ szNzAzT0 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO ) ),
    inference(simp,[status(thm)],[611]) ).

thf(720,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( ( aElementOf0 @ sk1 @ szNzAzT0 )
     != ( aElementOf0 @ xk @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,613]) ).

thf(726,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( sk1 != xk )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[720]) ).

thf(729,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( sk1 != xk ) ),
    inference(simp,[status(thm)],[726]) ).

thf(19081,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,217]) ).

thf(19082,plain,
    aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) @ szNzAzT0,
    inference(pattern_uni,[status(thm)],[19081:[bind(A,$thf( sk31 @ xK ))]]) ).

thf(245,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ( A = slcrc0 )
      | ~ ( aElementOf0 @ B @ A )
      | ( aElementOf0 @ ( sk6 @ B @ A ) @ A )
      | ( B
        = ( szmzizndt0 @ A ) ) ),
    inference(cnf,[status(esa)],[242]) ).

thf(251,plain,
    ! [B: $i,A: $i] :
      ( ( A = slcrc0 )
      | ( B
        = ( szmzizndt0 @ A ) )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ A )
      | ( aElementOf0 @ ( sk6 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[245]) ).

thf(252,plain,
    ! [B: $i,A: $i] :
      ( ( A = slcrc0 )
      | ( B
        = ( szmzizndt0 @ A ) )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ A )
      | ( aElementOf0 @ ( sk6 @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[251]) ).

thf(19788,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,7910]) ).

thf(19886,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
    | ( ( slbdtrb0 @ xk )
     != xS ) ),
    inference(simp,[status(thm)],[19788]) ).

thf(19642,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,7840]) ).

thf(19731,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
    | ( ( slbdtrb0 @ xK )
     != xS ) ),
    inference(simp,[status(thm)],[19642]) ).

thf(222,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ~ ( isFinite0 @ A )
      | ~ ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) )
      | ( ( sbrdtbr0 @ ( sk5 @ B @ A ) )
        = B ) ),
    inference(cnf,[status(esa)],[221]) ).

thf(224,plain,
    ! [B: $i,A: $i] :
      ( ( ( sbrdtbr0 @ ( sk5 @ B @ A ) )
        = B )
      | ~ ( aSet0 @ A )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ~ ( isFinite0 @ A )
      | ~ ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) ),
    inference(lifteq,[status(thm)],[222]) ).

thf(43,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aSet0 @ B ) )
     => ( ~ ( aElementOf0 @ A @ B )
       => ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).

thf(229,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aSet0 @ B ) )
     => ( ~ ( aElementOf0 @ A @ B )
       => ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(8251,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
     != ( aSet0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[7814,4286]) ).

thf(8255,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ xS )
    | ( ( slbdtrb0 @ sk1 )
     != xS ) ),
    inference(simp,[status(thm)],[8251]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i,C: $i] :
          ( ( ( aSet0 @ B )
            & ( aSet0 @ C )
            & ( A != sz00 ) )
         => ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
              & ( ( slbdtsldtrb0 @ B @ A )
               != slcrc0 ) )
           => ( aSubsetOf0 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelSub) ).

thf(566,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i,C: $i] :
          ( ( ( aSet0 @ B )
            & ( aSet0 @ C )
            & ( A != sz00 ) )
         => ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
              & ( ( slbdtsldtrb0 @ B @ A )
               != slcrc0 ) )
           => ( aSubsetOf0 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(20046,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[873,218]) ).

thf(20047,plain,
    ( ( xk = sz00 )
    | ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) ) ),
    inference(pattern_uni,[status(thm)],[20046:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(7841,plain,
    ! [A: $i] :
      ( ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 )
      | ( ( aSet0 @ ( slbdtrb0 @ xK ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7770,108]) ).

thf(7842,plain,
    ( ( ( sbrdtbr0 @ ( slbdtrb0 @ xK ) )
     != sz00 )
    | ( ( slbdtrb0 @ xK )
      = slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[7841:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).

thf(2055,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( aSubsetOf0 @ A @ B )
      | ~ ( aSubsetOf0 @ B @ A )
      | ( B != slcrc0 )
      | ( A != xS ) ),
    inference(paramod_ordered,[status(thm)],[143,660]) ).

thf(2056,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ xS )
      | ~ ( aSet0 @ A )
      | ~ ( aSubsetOf0 @ xS @ A )
      | ~ ( aSubsetOf0 @ A @ xS )
      | ( A != slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[2055:[bind(A,$thf( xS ))]]) ).

thf(2929,plain,
    ( ~ ( aSet0 @ xS )
    | ~ ( aSet0 @ slcrc0 )
    | ~ ( aSubsetOf0 @ xS @ slcrc0 )
    | ~ ( aSubsetOf0 @ slcrc0 @ xS ) ),
    inference(simp,[status(thm)],[2056]) ).

thf(3253,plain,
    ( ~ ( aSet0 @ xS )
    | ~ $true
    | ~ ( aSubsetOf0 @ xS @ slcrc0 )
    | ~ ( aSubsetOf0 @ slcrc0 @ xS ) ),
    inference(rewrite,[status(thm)],[2929,372]) ).

thf(3254,plain,
    ( ~ ( aSet0 @ xS )
    | ~ ( aSubsetOf0 @ xS @ slcrc0 )
    | ~ ( aSubsetOf0 @ slcrc0 @ xS ) ),
    inference(simp,[status(thm)],[3253]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ! [C: $i] :
              ( ( C
                = ( sdtlcdtrc0 @ A @ B ) )
            <=> ( ( aSet0 @ C )
                & ! [D: $i] :
                    ( ( aElementOf0 @ D @ C )
                  <=> ? [E: $i] :
                        ( ( aElementOf0 @ E @ B )
                        & ( ( sdtlpdtrp0 @ A @ E )
                          = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).

thf(388,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ! [C: $i] :
              ( ( ( C
                  = ( sdtlcdtrc0 @ A @ B ) )
               => ( ( aSet0 @ C )
                  & ! [D: $i] :
                      ( ( ( aElementOf0 @ D @ C )
                       => ? [E: $i] :
                            ( ( aElementOf0 @ E @ B )
                            & ( ( sdtlpdtrp0 @ A @ E )
                              = D ) ) )
                      & ( ? [E: $i] :
                            ( ( aElementOf0 @ E @ B )
                            & ( ( sdtlpdtrp0 @ A @ E )
                              = D ) )
                       => ( aElementOf0 @ D @ C ) ) ) ) )
              & ( ( ( aSet0 @ C )
                  & ! [D: $i] :
                      ( ( ( aElementOf0 @ D @ C )
                       => ? [E: $i] :
                            ( ( aElementOf0 @ E @ B )
                            & ( ( sdtlpdtrp0 @ A @ E )
                              = D ) ) )
                      & ( ? [E: $i] :
                            ( ( aElementOf0 @ E @ B )
                            & ( ( sdtlpdtrp0 @ A @ E )
                              = D ) )
                       => ( aElementOf0 @ D @ C ) ) ) )
               => ( C
                  = ( sdtlcdtrc0 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(12814,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xe ) ) ),
    inference(paramod_ordered,[status(thm)],[167,7368]) ).

thf(12867,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( xc != xe ) ),
    inference(simp,[status(thm)],[12814]) ).

thf(13116,plain,
    ( ( xc != xe )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,12867]) ).

thf(13163,plain,
    ( ( xc != xe )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[13116]) ).

thf(172,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk4 @ B @ A ) ) @ A )
      | ( B
        = ( slbdtrb0 @ A ) ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(187,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk4 @ B @ A ) ) @ A ) ),
    inference(lifteq,[status(thm)],[172]) ).

thf(188,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ( sdtlseqdt0 @ ( szszuzczcdt0 @ ( sk4 @ B @ A ) ) @ A ) ),
    inference(simp,[status(thm)],[187]) ).

thf(1360,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ xT )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,131]) ).

thf(1361,plain,
    aElement0 @ ( sbrdtbr0 @ xT ),
    inference(pattern_uni,[status(thm)],[1360:[bind(A,$thf( xT ))]]) ).

thf(665,plain,
    ! [A: $i] :
      ( ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 )
      | ( ( aSet0 @ xO )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[199,108]) ).

thf(666,plain,
    ( ( ( sbrdtbr0 @ xO )
     != sz00 )
    | ( xO = slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[665:[bind(A,$thf( xO ))]]) ).

thf(3728,plain,
    ( ( sbrdtbr0 @ xO )
   != sz00 ),
    inference(simplifyReflect,[status(thm)],[666,607]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( isFinite0 @ A )
        & ( A != slcrc0 ) )
     => ! [B: $i] :
          ( ( B
            = ( szmzazxdt0 @ A ) )
        <=> ( ( aElementOf0 @ B @ A )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ A )
               => ( sdtlseqdt0 @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).

thf(489,plain,
    ! [A: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( isFinite0 @ A )
        & ( A != slcrc0 ) )
     => ! [B: $i] :
          ( ( ( B
              = ( szmzazxdt0 @ A ) )
           => ( ( aElementOf0 @ B @ A )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ A )
                 => ( sdtlseqdt0 @ C @ B ) ) ) )
          & ( ( ( aElementOf0 @ B @ A )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ A )
                 => ( sdtlseqdt0 @ C @ B ) ) )
           => ( B
              = ( szmzazxdt0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(7326,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( isCountable0 @ ( szDzozmdt0 @ xc ) )
     != ( isCountable0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[198,4298]) ).

thf(7365,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != xO ) ),
    inference(simp,[status(thm)],[7326]) ).

thf(69897,plain,
    ( ( xN != xe )
    | ( ( isCountable0 @ ( sdtlpdtrp0 @ xe @ xK ) )
     != ( isCountable0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[69578,4360]) ).

thf(69954,plain,
    ( ( xN != xe )
    | ( ( sdtlpdtrp0 @ xe @ xK )
     != xT ) ),
    inference(simp,[status(thm)],[69897]) ).

thf(847,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( aElementOf0 @ sz00 @ xO )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[517,101]) ).

thf(848,plain,
    ( ~ ( aElementOf0 @ sk1 @ szNzAzT0 )
    | ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO ) ),
    inference(pattern_uni,[status(thm)],[847:[bind(A,$thf( sk1 ))]]) ).

thf(1598,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
     != ( aElementOf0 @ sk1 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,848]) ).

thf(1643,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( ( sk31 @ xK )
     != sk1 )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[1598]) ).

thf(1659,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( ( sk31 @ xK )
     != sk1 ) ),
    inference(simp,[status(thm)],[1643]) ).

thf(38099,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ xO ) ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[32270,131]) ).

thf(38100,plain,
    ( ( xO != szNzAzT0 )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( szmzizndt0 @ xO ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[38099:[bind(A,$thf( slbdtrb0 @ ( szmzizndt0 @ xO ) ))]]) ).

thf(42500,plain,
    ( ( xk != sz00 )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[362,42399]) ).

thf(42554,plain,
    ( ( xk != sz00 )
    | ( ( slbdtrb0 @ xk )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[42500]) ).

thf(39631,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,259]) ).

thf(39632,plain,
    aElementOf0 @ ( sk7 @ xK ) @ xT,
    inference(pattern_uni,[status(thm)],[39631:[bind(A,$thf( xK ))]]) ).

thf(23077,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
    | ( sdtlseqdt0 @ xk @ sz00 )
    | ( xk != xk ) ),
    inference(paramod_ordered,[status(thm)],[7766,22970]) ).

thf(23078,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
    | ( sdtlseqdt0 @ xk @ sz00 ) ),
    inference(pattern_uni,[status(thm)],[23077:[]]) ).

thf(1724,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xN )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[593,1668]) ).

thf(1744,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( xN != xc ) ),
    inference(simp,[status(thm)],[1724]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).

thf(210,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(211,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ A @ B )
      | ~ ( sdtlseqdt0 @ B @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[210]) ).

thf(212,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ A @ B )
      | ~ ( sdtlseqdt0 @ B @ A ) ),
    inference(lifteq,[status(thm)],[211]) ).

thf(699,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( ( aElementOf0 @ sk1 @ szNzAzT0 )
     != ( aElementOf0 @ xK @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,613]) ).

thf(704,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( sk1 != xK )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[699]) ).

thf(706,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( sk1 != xK ) ),
    inference(simp,[status(thm)],[704]) ).

thf(42282,plain,
    ( ( ( slbdtrb0 @ xk )
     != slcrc0 )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,19879]) ).

thf(42396,plain,
    ( ( ( slbdtrb0 @ xk )
     != slcrc0 )
    | ( ( slbdtrb0 @ xk )
     != xS ) ),
    inference(simp,[status(thm)],[42282]) ).

thf(12791,plain,
    ( ( ( szDzozmdt0 @ xc )
     != szNzAzT0 )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,7368]) ).

thf(12859,plain,
    ( ( ( szDzozmdt0 @ xc )
     != szNzAzT0 )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[12791]) ).

thf(10833,plain,
    ! [A: $i] :
      ( ( ( szszuzczcdt0 @ sz00 )
        = xK )
      | ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7781,131]) ).

thf(10834,plain,
    ( ( ( szszuzczcdt0 @ sz00 )
      = xK )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[10833:[bind(A,$thf( slbdtrb0 @ ( sk31 @ xk ) ))]]) ).

thf(29102,plain,
    ( ( ( slbdtrb0 @ xK )
     != xO )
    | ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,19733]) ).

thf(29114,plain,
    ( ( ( slbdtrb0 @ xK )
     != xO )
    | ( ( slbdtrb0 @ xK )
     != xT ) ),
    inference(simp,[status(thm)],[29102]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( A
       != ( szszuzczcdt0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).

thf(503,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( A
       != ( szszuzczcdt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(13156,plain,
    ( ( xc != xe )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,12867]) ).

thf(13167,plain,
    ( ( xc != xe )
    | ( ( szDzozmdt0 @ xc )
     != xT ) ),
    inference(simp,[status(thm)],[13156]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( sdtlseqdt0 @ sz00 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).

thf(569,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( sdtlseqdt0 @ sz00 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(20255,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xK ) )
   != ( isCountable0 @ xT ) ),
    inference(paramod_ordered,[status(thm)],[20056,4360]) ).

thf(20290,plain,
    ( ( sdtlpdtrp0 @ xN @ xK )
   != xT ),
    inference(simp,[status(thm)],[20255]) ).

thf(19827,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[198,7910]) ).

thf(19878,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
    | ( ( slbdtrb0 @ xk )
     != xO ) ),
    inference(simp,[status(thm)],[19827]) ).

thf(12342,plain,
    ( ( ( szDzozmdt0 @ xc )
     != xO )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,7365]) ).

thf(12361,plain,
    ( ( ( szDzozmdt0 @ xc )
     != xO )
    | ( ( szDzozmdt0 @ xc )
     != xT ) ),
    inference(simp,[status(thm)],[12342]) ).

thf(23085,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( sdtlseqdt0 @ xk @ sz00 )
    | ( xk != xk ) ),
    inference(paramod_ordered,[status(thm)],[873,22970]) ).

thf(23086,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( sdtlseqdt0 @ xk @ sz00 ) ),
    inference(pattern_uni,[status(thm)],[23085:[]]) ).

thf(299,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ( C
       != ( sdtexdt0 @ A @ B ) )
      | ( ( szDzozmdt0 @ C )
        = B ) ),
    inference(cnf,[status(esa)],[298]) ).

thf(310,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtexdt0 @ A @ B ) )
      | ( ( szDzozmdt0 @ C )
        = B )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) ) ),
    inference(lifteq,[status(thm)],[299]) ).

thf(311,plain,
    ! [B: $i,A: $i] :
      ( ( ( szDzozmdt0 @ ( sdtexdt0 @ A @ B ) )
        = B )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) ) ),
    inference(simp,[status(thm)],[310]) ).

thf(815,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( ( szDzozmdt0 @ xN )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[593,117]) ).

thf(824,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( xN != xc ) ),
    inference(simp,[status(thm)],[815]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isCountable0 @ B ) )
         => ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCConsSet) ).

thf(148,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isCountable0 @ B ) )
         => ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1727,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xe ) ) ),
    inference(paramod_ordered,[status(thm)],[167,1668]) ).

thf(1747,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( xc != xe ) ),
    inference(simp,[status(thm)],[1727]) ).

thf(161,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ( sdtlseqdt0 @ A @ B )
      | ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ),
    inference(cnf,[status(esa)],[160]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).

thf(444,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( isFinite0 @ A ) )
     => ? [B: $i] :
          ( ( aElementOf0 @ B @ szNzAzT0 )
          & ( aSubsetOf0 @ A @ ( slbdtrb0 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinSubSeg) ).

thf(375,plain,
    ! [A: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( isFinite0 @ A ) )
     => ? [B: $i] :
          ( ( aElementOf0 @ B @ szNzAzT0 )
          & ( aSubsetOf0 @ A @ ( slbdtrb0 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(39608,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[101,259]) ).

thf(39817,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( sk1 != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[39608]) ).

thf(39888,plain,
    ( ( aElementOf0 @ ( sk7 @ sk1 ) @ xT )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[39817]) ).

thf(170,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ~ ( aElementOf0 @ ( sk4 @ B @ A ) @ B )
      | ( B
        = ( slbdtrb0 @ A ) ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(179,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ~ ( aElementOf0 @ ( sk4 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[170]) ).

thf(180,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ~ ( aElementOf0 @ ( sk4 @ B @ A ) @ B ) ),
    inference(simp,[status(thm)],[179]) ).

thf(271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ C )
      | ~ ( sk8 @ A @ B @ C )
      | ( C
        = ( sdtmndt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ C )
      | ~ ( sk8 @ A @ B @ C ) ),
    inference(lifteq,[status(thm)],[271]) ).

thf(296,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ C )
      | ~ ( sk8 @ A @ B @ C ) ),
    inference(simp,[status(thm)],[295]) ).

thf(149,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElement0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( isCountable0 @ B )
      | ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[148]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
      <=> ( isFinite0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).

thf(584,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
         => ( isFinite0 @ A ) )
        & ( ( isFinite0 @ A )
         => ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
            & ( isCountable0 @ B ) )
         => ! [C: $i] :
              ( ( ( aSet0 @ C )
                & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
             => ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4331) ).

thf(562,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
            & ( isCountable0 @ B ) )
         => ! [C: $i] :
              ( ( ( aSet0 @ C )
                & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
             => ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(68,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( sdtlseqdt0 @ B @ A )
       => ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).

thf(423,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( sdtlseqdt0 @ B @ A )
       => ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(22944,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[873,226]) ).

thf(22945,plain,
    ( ( xk = sz00 )
    | ( sdtlseqdt0 @ ( sk31 @ xk ) @ ( sk31 @ xk ) ) ),
    inference(pattern_uni,[status(thm)],[22944:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ~ ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ C )
      | ( C
        = ( sdtmndt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(285,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ~ ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ C ) ),
    inference(lifteq,[status(thm)],[267]) ).

thf(286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ~ ( aElementOf0 @ ( sk10 @ C @ B @ A ) @ C ) ),
    inference(simp,[status(thm)],[285]) ).

thf(825,plain,
    ( ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
   != ( isCountable0 @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[320,647]) ).

thf(826,plain,
    ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
   != slcrc0 ),
    inference(simp,[status(thm)],[825]) ).

thf(12848,plain,
    ( ( ( szDzozmdt0 @ xc )
     != szNzAzT0 )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,7368]) ).

thf(12862,plain,
    ( ( ( szDzozmdt0 @ xc )
     != szNzAzT0 )
    | ( ( szDzozmdt0 @ xc )
     != xT ) ),
    inference(simp,[status(thm)],[12848]) ).

thf(300,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ( C
       != ( sdtexdt0 @ A @ B ) )
      | ~ ( aElementOf0 @ D @ B )
      | ( ( sdtlpdtrp0 @ C @ D )
        = ( sdtlpdtrp0 @ A @ D ) ) ),
    inference(cnf,[status(esa)],[298]) ).

thf(312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtexdt0 @ A @ B ) )
      | ( ( sdtlpdtrp0 @ C @ D )
        = ( sdtlpdtrp0 @ A @ D ) )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ~ ( aElementOf0 @ D @ B ) ),
    inference(lifteq,[status(thm)],[300]) ).

thf(313,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sdtlpdtrp0 @ ( sdtexdt0 @ A @ B ) @ C )
        = ( sdtlpdtrp0 @ A @ C ) )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ~ ( aElementOf0 @ C @ B ) ),
    inference(simp,[status(thm)],[312]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( ( isFinite0 @ A )
       => $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinRel) ).

thf(144,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(19864,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
    | ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,7910]) ).

thf(19881,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xk ) )
    | ( ( slbdtrb0 @ xk )
     != xT ) ),
    inference(simp,[status(thm)],[19864]) ).

thf(50155,plain,
    ( ( ( slbdtrb0 @ xk )
     != xT )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,19881]) ).

thf(50265,plain,
    ( ( ( slbdtrb0 @ xk )
     != xT )
    | ( ( slbdtrb0 @ xk )
     != xS ) ),
    inference(simp,[status(thm)],[50155]) ).

thf(7871,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ ( slbdtrb0 @ xK ) )
     != ( aSet0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[7770,4286]) ).

thf(7875,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( slbdtrb0 @ xK )
     != xS ) ),
    inference(simp,[status(thm)],[7871]) ).

thf(4303,plain,
    ! [A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ( ( isCountable0 @ xO )
       != ( isCountable0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[198,159]) ).

thf(4304,plain,
    ( ~ ( aSet0 @ xO )
    | ~ ( isFinite0 @ xO ) ),
    inference(pattern_uni,[status(thm)],[4303:[bind(A,$thf( xO ))]]) ).

thf(4572,plain,
    ( ~ $true
    | ~ ( isFinite0 @ xO ) ),
    inference(rewrite,[status(thm)],[4304,199]) ).

thf(4573,plain,
    ~ ( isFinite0 @ xO ),
    inference(simp,[status(thm)],[4572]) ).

thf(42501,plain,
    ( ( xk != sz00 )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[198,42399]) ).

thf(42546,plain,
    ( ( xk != sz00 )
    | ( ( slbdtrb0 @ xk )
     != xO ) ),
    inference(simp,[status(thm)],[42501]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 )
        & ( aElementOf0 @ C @ szNzAzT0 ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ C ) )
       => ( sdtlseqdt0 @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).

thf(235,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 )
        & ( aElementOf0 @ C @ szNzAzT0 ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ C ) )
       => ( sdtlseqdt0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ~ ( aElementOf0 @ C @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ A @ B )
      | ~ ( sdtlseqdt0 @ B @ C )
      | ( sdtlseqdt0 @ A @ C ) ),
    inference(cnf,[status(esa)],[235]) ).

thf(19826,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[362,7910]) ).

thf(19875,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xk ) )
    | ( ( slbdtrb0 @ xk )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[19826]) ).

thf(19718,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
    | ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,7840]) ).

thf(19741,plain,
    ( ~ ( isCountable0 @ ( slbdtrb0 @ xK ) )
    | ( ( slbdtrb0 @ xK )
     != xT ) ),
    inference(simp,[status(thm)],[19718]) ).

thf(31578,plain,
    ( ( ( slbdtrb0 @ xk )
     != szNzAzT0 )
    | ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,19875]) ).

thf(31590,plain,
    ( ( ( slbdtrb0 @ xk )
     != szNzAzT0 )
    | ( ( slbdtrb0 @ xk )
     != xT ) ),
    inference(simp,[status(thm)],[31578]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).

thf(113,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(694,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,102]) ).

thf(695,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xK )
     != sk1 )
    | ~ ( aElementOf0 @ xK @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
    inference(pattern_uni,[status(thm)],[694:[bind(A,$thf( xK ))]]) ).

thf(732,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xK )
     != sk1 )
    | ( ( aElementOf0 @ sk1 @ xO )
     != ( aElementOf0 @ xK @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[101,695]) ).

thf(736,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xK )
     != sk1 )
    | ( sk1 != xK )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO ) ),
    inference(simp,[status(thm)],[732]) ).

thf(31896,plain,
    ! [A: $i] :
      ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[31786,218]) ).

thf(31897,plain,
    isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[31896:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).

thf(663,plain,
    ! [A: $i] :
      ( ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 )
      | ( ( aSet0 @ xT )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,108]) ).

thf(664,plain,
    ( ( ( sbrdtbr0 @ xT )
     != sz00 )
    | ( xT = slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[663:[bind(A,$thf( xT ))]]) ).

thf(768,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
     != ( aElementOf0 @ A @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[321,374]) ).

thf(776,plain,
    ! [A: $i] :
      ( ( ( szDzizrdt0 @ xd )
       != A )
      | ( xT != slcrc0 ) ),
    inference(simp,[status(thm)],[768]) ).

thf(781,plain,
    xT != slcrc0,
    inference(simp,[status(thm)],[776]) ).

thf(3710,plain,
    ( ( sbrdtbr0 @ xT )
   != sz00 ),
    inference(simplifyReflect,[status(thm)],[664,781]) ).

thf(451,plain,
    aFunction0 @ xC,
    inference(cnf,[status(esa)],[446]) ).

thf(4361,plain,
    ( ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
   != ( isCountable0 @ xT ) ),
    inference(paramod_ordered,[status(thm)],[320,4360]) ).

thf(4374,plain,
    ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
   != xT ),
    inference(simp,[status(thm)],[4361]) ).

thf(205,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) )
      | ( ( sdtlpdtrp0 @ xd @ A )
        = ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[204]) ).

thf(208,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
        = ( sdtlpdtrp0 @ xd @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ~ ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ),
    inference(lifteq,[status(thm)],[205]) ).

thf(1570,plain,
    ! [A: $i] :
      ( ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,517]) ).

thf(1571,plain,
    ( ( ( sk31 @ xK )
      = sz00 )
    | ( aElementOf0 @ ( sk31 @ ( sk31 @ xK ) ) @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[1570:[bind(A,$thf( sk31 @ xK ))]]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aElement0 @ B )
         => ( ~ ( aElementOf0 @ B @ A )
           => ( ( sbrdtbr0 @ ( sdtpldt0 @ A @ B ) )
              = ( szszuzczcdt0 @ ( sbrdtbr0 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).

thf(599,plain,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aElement0 @ B )
         => ( ~ ( aElementOf0 @ B @ A )
           => ( ( sbrdtbr0 @ ( sdtpldt0 @ A @ B ) )
              = ( szszuzczcdt0 @ ( sbrdtbr0 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(14126,plain,
    ( ( xO != szNzAzT0 )
    | ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( slbdtrb0 @ sk1 )
     != ( slbdtrb0 @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[137,8219]) ).

thf(14223,plain,
    ( ( aSubsetOf0 @ slcrc0 @ ( slbdtrb0 @ sk1 ) )
    | ( xO != szNzAzT0 )
    | ( sk1 != sz00 ) ),
    inference(simp,[status(thm)],[14126]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ A )
         => ( isFinite0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).

thf(103,plain,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ A )
         => ( isFinite0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
          & ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
       => ( ( aElement0 @ ( szDzizrdt0 @ A ) )
          & ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDirichlet) ).

thf(213,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
          & ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
       => ( ( aElement0 @ ( szDzizrdt0 @ A ) )
          & ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(7942,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ xk ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7779,131]) ).

thf(7943,plain,
    aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ xk ) ),
    inference(pattern_uni,[status(thm)],[7942:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).

thf(9121,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) )
    | ( xk != xk ) ),
    inference(paramod_ordered,[status(thm)],[873,7943]) ).

thf(9122,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) ) ),
    inference(pattern_uni,[status(thm)],[9121:[]]) ).

thf(18912,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( aElement0 @ ( sbrdtbr0 @ slcrc0 ) ) ),
    inference(rewrite,[status(thm)],[9122,137]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFunSort) ).

thf(155,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(827,plain,
    aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ szNzAzT0 ) @ xT,
    inference(rewrite,[status(thm)],[202,209]) ).

thf(265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ( C
       != ( sdtmndt0 @ A @ B ) )
      | ~ ( aElementOf0 @ D @ C )
      | ( aElement0 @ D ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(277,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElementOf0 @ D @ C )
      | ( aElement0 @ D ) ),
    inference(lifteq,[status(thm)],[265]) ).

thf(278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aElementOf0 @ C @ ( sdtmndt0 @ A @ B ) )
      | ( aElement0 @ C ) ),
    inference(simp,[status(thm)],[277]) ).

thf(31628,plain,
    ( ( ( slbdtrb0 @ xk )
     != xO )
    | ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,19878]) ).

thf(31755,plain,
    ( ( ( slbdtrb0 @ xk )
     != xO )
    | ( ( slbdtrb0 @ xk )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[31628]) ).

thf(223,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ~ ( isFinite0 @ A )
      | ~ ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) )
      | ( aSubsetOf0 @ ( sk5 @ B @ A ) @ A ) ),
    inference(cnf,[status(esa)],[221]) ).

thf(20717,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) )
   != ( isCountable0 @ xT ) ),
    inference(paramod_ordered,[status(thm)],[20059,4360]) ).

thf(20770,plain,
    ( ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) )
   != xT ),
    inference(simp,[status(thm)],[20717]) ).

thf(1661,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ slcrc0 )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[372,135]) ).

thf(1662,plain,
    aSubsetOf0 @ slcrc0 @ slcrc0,
    inference(pattern_uni,[status(thm)],[1661:[bind(A,$thf( slcrc0 ))]]) ).

thf(24497,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
     != ( isCountable0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[198,8213]) ).

thf(24553,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( slbdtrb0 @ sk1 )
     != xO ) ),
    inference(simp,[status(thm)],[24497]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isFinite0 @ B ) )
         => ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).

thf(111,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aSet0 @ B )
            & ( isFinite0 @ B ) )
         => ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(112,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElement0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( isFinite0 @ B )
      | ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[111]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( aSubsetOf0 @ B @ szNzAzT0 )
            & ( isCountable0 @ B ) )
         => ! [C: $i] :
              ( ( ( aFunction0 @ C )
                & ( ( szDzozmdt0 @ C )
                  = ( slbdtsldtrb0 @ B @ A ) )
                & ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) )
             => ( ( iLess0 @ A @ xK )
               => ? [D: $i] :
                    ( ( aElementOf0 @ D @ xT )
                    & ? [E: $i] :
                        ( ( aSubsetOf0 @ E @ B )
                        & ( isCountable0 @ E )
                        & ! [F: $i] :
                            ( ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) )
                           => ( ( sdtlpdtrp0 @ C @ F )
                              = D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3398) ).

thf(553,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( aSubsetOf0 @ B @ szNzAzT0 )
            & ( isCountable0 @ B ) )
         => ! [C: $i] :
              ( ( ( aFunction0 @ C )
                & ( ( szDzozmdt0 @ C )
                  = ( slbdtsldtrb0 @ B @ A ) )
                & ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) )
             => ( ( iLess0 @ A @ xK )
               => ? [D: $i] :
                    ( ( aElementOf0 @ D @ xT )
                    & ? [E: $i] :
                        ( ( aSubsetOf0 @ E @ B )
                        & ( isCountable0 @ E )
                        & ! [F: $i] :
                            ( ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) )
                           => ( ( sdtlpdtrp0 @ C @ F )
                              = D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(22952,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,226]) ).

thf(22953,plain,
    sdtlseqdt0 @ ( sk31 @ xK ) @ ( sk31 @ xK ),
    inference(pattern_uni,[status(thm)],[22952:[bind(A,$thf( sk31 @ xK ))]]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).

thf(487,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(77,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ! [C: $i] :
          ( ( C
            = ( slbdtsldtrb0 @ A @ B ) )
        <=> ( ( aSet0 @ C )
            & ! [D: $i] :
                ( ( aElementOf0 @ D @ C )
              <=> ( ( aSubsetOf0 @ D @ A )
                  & ( ( sbrdtbr0 @ D )
                    = B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).

thf(458,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ! [C: $i] :
          ( ( ( C
              = ( slbdtsldtrb0 @ A @ B ) )
           => ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aSubsetOf0 @ D @ A )
                      & ( ( sbrdtbr0 @ D )
                        = B ) ) )
                  & ( ( ( aSubsetOf0 @ D @ A )
                      & ( ( sbrdtbr0 @ D )
                        = B ) )
                   => ( aElementOf0 @ D @ C ) ) ) ) )
          & ( ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aSubsetOf0 @ D @ A )
                      & ( ( sbrdtbr0 @ D )
                        = B ) ) )
                  & ( ( ( aSubsetOf0 @ D @ A )
                      & ( ( sbrdtbr0 @ D )
                        = B ) )
                   => ( aElementOf0 @ D @ C ) ) ) )
           => ( C
              = ( slbdtsldtrb0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(818,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xd ) ) ),
    inference(paramod_ordered,[status(thm)],[209,117]) ).

thf(823,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( xc != xd ) ),
    inference(simp,[status(thm)],[818]) ).

thf(171,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ( aElementOf0 @ ( sk4 @ B @ A ) @ szNzAzT0 )
      | ( B
        = ( slbdtrb0 @ A ) ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(193,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ( aElementOf0 @ ( sk4 @ B @ A ) @ szNzAzT0 ) ),
    inference(lifteq,[status(thm)],[171]) ).

thf(194,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( sk2 @ A @ B )
      | ( aElementOf0 @ ( sk4 @ B @ A ) @ szNzAzT0 ) ),
    inference(simp,[status(thm)],[193]) ).

thf(1726,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xe ) ) ),
    inference(paramod_ordered,[status(thm)],[167,1668]) ).

thf(1748,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( xc != xe ) ),
    inference(simp,[status(thm)],[1726]) ).

thf(266,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ~ ( aElement0 @ ( sk9 @ C @ B @ A ) )
      | ~ ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ A )
      | ( ( sk9 @ C @ B @ A )
        = B )
      | ~ ( sk8 @ A @ B @ C )
      | ( C
        = ( sdtmndt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk9 @ C @ B @ A )
        = B )
      | ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ~ ( aElement0 @ ( sk9 @ C @ B @ A ) )
      | ~ ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ A )
      | ~ ( sk8 @ A @ B @ C ) ),
    inference(lifteq,[status(thm)],[266]) ).

thf(282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk9 @ C @ B @ A )
        = B )
      | ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ~ ( aElement0 @ ( sk9 @ C @ B @ A ) )
      | ~ ( aElementOf0 @ ( sk9 @ C @ B @ A ) @ A )
      | ~ ( sk8 @ A @ B @ C ) ),
    inference(simp,[status(thm)],[281]) ).

thf(4366,plain,
    ( ( isCountable0 @ xT )
   != ( isCountable0 @ xO ) ),
    inference(paramod_ordered,[status(thm)],[198,4360]) ).

thf(4377,plain,
    xT != xO,
    inference(simp,[status(thm)],[4366]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B )
        & ( aSet0 @ C ) )
     => ( ( ( aSubsetOf0 @ A @ B )
          & ( aSubsetOf0 @ B @ C ) )
       => ( aSubsetOf0 @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).

thf(150,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B )
        & ( aSet0 @ C ) )
     => ( ( ( aSubsetOf0 @ A @ B )
          & ( aSubsetOf0 @ B @ C ) )
       => ( aSubsetOf0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(1728,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xd ) ) ),
    inference(paramod_ordered,[status(thm)],[209,1668]) ).

thf(1743,plain,
    ( ( aSubsetOf0 @ szNzAzT0 @ ( szDzozmdt0 @ xc ) )
    | ( xc != xd ) ),
    inference(simp,[status(thm)],[1728]) ).

thf(31844,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
      | ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[31786,166]) ).

thf(31845,plain,
    ( ( sdtlpdtrp0 @ xe @ ( szmzizndt0 @ szNzAzT0 ) )
    = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) ) ),
    inference(pattern_uni,[status(thm)],[31844:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).

thf(4324,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
     != ( aSet0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[1251,4286]) ).

thf(4346,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( szDzozmdt0 @ xc )
     != xS ) ),
    inference(simp,[status(thm)],[4324]) ).

thf(174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ( B
       != ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ C @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A )
      | ( aElementOf0 @ C @ B ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(181,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ C @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A )
      | ( aElementOf0 @ C @ B ) ),
    inference(lifteq,[status(thm)],[174]) ).

thf(182,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ szNzAzT0 )
      | ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A )
      | ( aElementOf0 @ B @ ( slbdtrb0 @ A ) ) ),
    inference(simp,[status(thm)],[181]) ).

thf(20236,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xK ) )
   != ( isCountable0 @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[20056,647]) ).

thf(20287,plain,
    ( ( sdtlpdtrp0 @ xN @ xK )
   != slcrc0 ),
    inference(simp,[status(thm)],[20236]) ).

thf(19063,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[101,217]) ).

thf(19197,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
      | ( sk1 != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[19063]) ).

thf(19248,plain,
    ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ sk1 ) @ szNzAzT0 )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[19197]) ).

thf(31464,plain,
    ( ( ( slbdtrb0 @ xk )
     != szNzAzT0 )
    | ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,19875]) ).

thf(31595,plain,
    ( ( ( slbdtrb0 @ xk )
     != szNzAzT0 )
    | ( ( slbdtrb0 @ xk )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[31464]) ).

thf(20819,plain,
    ( ( xO != szNzAzT0 )
    | ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ sk1 ) )
     != ( isCountable0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[20194,647]) ).

thf(20883,plain,
    ( ( xO != szNzAzT0 )
    | ( ( sdtlpdtrp0 @ xN @ sk1 )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[20819]) ).

thf(1589,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( ( aElementOf0 @ sk1 @ szNzAzT0 )
     != ( aElementOf0 @ xk @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[508,848]) ).

thf(1642,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( sk1 != xk )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[1589]) ).

thf(1658,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( sk1 != xk ) ),
    inference(simp,[status(thm)],[1642]) ).

thf(23083,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( sdtlseqdt0 @ sz00 @ xk )
    | ( xk != xk ) ),
    inference(paramod_ordered,[status(thm)],[873,22970]) ).

thf(23084,plain,
    ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
    | ( sdtlseqdt0 @ sz00 @ xk ) ),
    inference(pattern_uni,[status(thm)],[23083:[]]) ).

thf(34100,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[31912,131]) ).

thf(34101,plain,
    aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ) ),
    inference(pattern_uni,[status(thm)],[34100:[bind(A,$thf( slbdtrb0 @ ( szmzizndt0 @ szNzAzT0 ) ))]]) ).

thf(19680,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ xK ) )
     != ( isCountable0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[362,7840]) ).

thf(19738,plain,
    ( ~ ( isFinite0 @ ( slbdtrb0 @ xK ) )
    | ( ( slbdtrb0 @ xK )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[19680]) ).

thf(31254,plain,
    ( ( ( slbdtrb0 @ xK )
     != szNzAzT0 )
    | ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,19738]) ).

thf(31269,plain,
    ( ( ( slbdtrb0 @ xK )
     != szNzAzT0 )
    | ( ( slbdtrb0 @ xK )
     != xT ) ),
    inference(simp,[status(thm)],[31254]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegFin) ).

thf(386,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(28872,plain,
    ( ( ( slbdtrb0 @ xK )
     != xS )
    | ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,19731]) ).

thf(28978,plain,
    ( ( ( slbdtrb0 @ xK )
     != xS )
    | ( ( slbdtrb0 @ xK )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[28872]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgElm) ).

thf(314,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
         => ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(95,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ! [C: $i] :
          ( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
            & ( isFinite0 @ C ) )
         => ? [D: $i] :
              ( ( aSubsetOf0 @ D @ A )
              & ( isFinite0 @ D )
              & ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelExtra) ).

thf(595,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ! [C: $i] :
          ( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
            & ( isFinite0 @ C ) )
         => ? [D: $i] :
              ( ( aSubsetOf0 @ D @ A )
              & ( isFinite0 @ D )
              & ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(608,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[101,102]) ).

thf(610,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
       != sk1 )
      | ~ ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
      | ( sk1 != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[608]) ).

thf(612,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ~ ( aElementOf0 @ sk1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[610]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ( ( isCountable0 @ A )
       => $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCntRel) ).

thf(154,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(12856,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( ( szDzozmdt0 @ xC )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[454,7368]) ).

thf(12868,plain,
    ( ~ ( isFinite0 @ ( szDzozmdt0 @ xc ) )
    | ( xC != xc ) ),
    inference(simp,[status(thm)],[12856]) ).

thf(1725,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( ( szDzozmdt0 @ xN )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[593,1668]) ).

thf(1749,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( xN != xc ) ),
    inference(simp,[status(thm)],[1725]) ).

thf(7783,plain,
    ! [A: $i] :
      ( ( ( sk31 @ xK )
        = sz00 )
      | ( aSet0 @ ( slbdtrb0 @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ ( sk31 @ xK ) ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1571,186]) ).

thf(7784,plain,
    ( ( ( sk31 @ xK )
      = sz00 )
    | ( aSet0 @ ( slbdtrb0 @ ( sk31 @ ( sk31 @ xK ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[7783:[bind(A,$thf( sk31 @ ( sk31 @ xK ) ))]]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isCountable0 @ A ) )
     => ! [B: $i] :
          ( ( ( aElementOf0 @ B @ szNzAzT0 )
            & ( B != sz00 ) )
         => ( isCountable0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelCSet) ).

thf(571,plain,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ( isCountable0 @ A ) )
     => ! [B: $i] :
          ( ( ( aElementOf0 @ B @ szNzAzT0 )
            & ( B != sz00 ) )
         => ( isCountable0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(39762,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[31786,259]) ).

thf(39763,plain,
    aElementOf0 @ ( sk7 @ ( szmzizndt0 @ szNzAzT0 ) ) @ xT,
    inference(pattern_uni,[status(thm)],[39762:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).

thf(7843,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ A @ A )
      | ( ( aSet0 @ ( slbdtrb0 @ xK ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7770,135]) ).

thf(7844,plain,
    aSubsetOf0 @ ( slbdtrb0 @ xK ) @ ( slbdtrb0 @ xK ),
    inference(pattern_uni,[status(thm)],[7843:[bind(A,$thf( slbdtrb0 @ xK ))]]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( iLess0 @ A @ B )
       => $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHSort) ).

thf(203,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ~ ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ szNzAzT0 )
         => ( ( slbdtsldtrb0 @ A @ B )
           != slcrc0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).

thf(581,plain,
    ! [A: $i] :
      ( ( ( aSet0 @ A )
        & ~ ( isFinite0 @ A ) )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ szNzAzT0 )
         => ( ( slbdtsldtrb0 @ A @ B )
           != slcrc0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1593,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( ( aElementOf0 @ sk1 @ szNzAzT0 )
     != ( aElementOf0 @ xK @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,848]) ).

thf(1636,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( sk1 != xK )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[1593]) ).

thf(1654,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( sk1 != xK ) ),
    inference(simp,[status(thm)],[1636]) ).

thf(104,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( isFinite0 @ A )
      | ~ ( aSubsetOf0 @ B @ A )
      | ( isFinite0 @ B ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(31870,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[31786,226]) ).

thf(31871,plain,
    sdtlseqdt0 @ ( szmzizndt0 @ szNzAzT0 ) @ ( szmzizndt0 @ szNzAzT0 ),
    inference(pattern_uni,[status(thm)],[31870:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).

thf(230,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElement0 @ A )
      | ~ ( aSet0 @ B )
      | ( aElementOf0 @ A @ B )
      | ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
        = B ) ),
    inference(cnf,[status(esa)],[229]) ).

thf(231,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
        = B )
      | ~ ( aElement0 @ A )
      | ~ ( aSet0 @ B )
      | ( aElementOf0 @ A @ B ) ),
    inference(lifteq,[status(thm)],[230]) ).

thf(4729,plain,
    ! [A: $i] :
      ( ( ( sdtlpdtrp0 @ xe @ A )
        = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
      | ( ( aElementOf0 @ ( sk31 @ xK ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[1560,166]) ).

thf(4730,plain,
    ( ( sdtlpdtrp0 @ xe @ ( sk31 @ xK ) )
    = ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xK ) ) ) ),
    inference(pattern_uni,[status(thm)],[4729:[bind(A,$thf( sk31 @ xK ))]]) ).

thf(34320,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) )
   != ( isCountable0 @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[31897,647]) ).

thf(34392,plain,
    ( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) )
   != slcrc0 ),
    inference(simp,[status(thm)],[34320]) ).

thf(32166,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[32083,226]) ).

thf(32236,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( xO != szNzAzT0 )
      | ( ( szmzizndt0 @ xO )
       != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32166]) ).

thf(32296,plain,
    ( ( sdtlseqdt0 @ ( szmzizndt0 @ xO ) @ ( szmzizndt0 @ xO ) )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[32236]) ).

thf(13216,plain,
    ( ( xC != xc )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,12868]) ).

thf(13224,plain,
    ( ( xC != xc )
    | ( ( szDzozmdt0 @ xc )
     != xT ) ),
    inference(simp,[status(thm)],[13216]) ).

thf(42469,plain,
    ( ( xk != sz00 )
    | ( ( isCountable0 @ ( slbdtrb0 @ xk ) )
     != ( isCountable0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[456,42399]) ).

thf(42551,plain,
    ( ( xk != sz00 )
    | ( ( slbdtrb0 @ xk )
     != xS ) ),
    inference(simp,[status(thm)],[42469]) ).

thf(1741,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( ( szDzozmdt0 @ xC )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[454,1668]) ).

thf(1745,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( xC != xc ) ),
    inference(simp,[status(thm)],[1741]) ).

thf(31789,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ ( szmzizndt0 @ szNzAzT0 ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[31786,217]) ).

thf(31790,plain,
    aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) @ szNzAzT0,
    inference(pattern_uni,[status(thm)],[31789:[bind(A,$thf( szmzizndt0 @ szNzAzT0 ))]]) ).

thf(7911,plain,
    ! [A: $i] :
      ( ( ( sbrdtbr0 @ A )
       != sz00 )
      | ( A = slcrc0 )
      | ( ( aSet0 @ ( slbdtrb0 @ xk ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7779,108]) ).

thf(7912,plain,
    ( ( ( sbrdtbr0 @ ( slbdtrb0 @ xk ) )
     != sz00 )
    | ( ( slbdtrb0 @ xk )
      = slcrc0 ) ),
    inference(pattern_uni,[status(thm)],[7911:[bind(A,$thf( slbdtrb0 @ xk ))]]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).

thf(114,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(19076,plain,
    ! [A: $i] :
      ( ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,217]) ).

thf(19077,plain,
    aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ xK ) @ szNzAzT0,
    inference(pattern_uni,[status(thm)],[19076:[bind(A,$thf( xK ))]]) ).

thf(34344,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) ) )
   != ( isCountable0 @ xT ) ),
    inference(paramod_ordered,[status(thm)],[31897,4360]) ).

thf(34402,plain,
    ( ( sdtlpdtrp0 @ xN @ ( szmzizndt0 @ szNzAzT0 ) )
   != xT ),
    inference(simp,[status(thm)],[34344]) ).

thf(8252,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( slbdtrb0 @ sk1 ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7814,131]) ).

thf(8253,plain,
    ( ( xO != szNzAzT0 )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sk1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8252:[bind(A,$thf( slbdtrb0 @ sk1 ))]]) ).

thf(82,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( sdtlseqdt0 @ A @ B )
      <=> ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegLess) ).

thf(510,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElementOf0 @ A @ szNzAzT0 )
        & ( aElementOf0 @ B @ szNzAzT0 ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
         => ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) ) )
        & ( ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) )
         => ( sdtlseqdt0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(39617,plain,
    ! [A: $i] :
      ( ( xO != szNzAzT0 )
      | ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ ( szmzizndt0 @ xO ) @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[32083,259]) ).

thf(39799,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( xO != szNzAzT0 )
      | ( ( szmzizndt0 @ xO )
       != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[39617]) ).

thf(39874,plain,
    ( ( aElementOf0 @ ( sk7 @ ( szmzizndt0 @ xO ) ) @ xT )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[39799]) ).

thf(207,plain,
    aFunction0 @ xd,
    inference(cnf,[status(esa)],[204]) ).

thf(20342,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xk ) )
   != ( isCountable0 @ slcrc0 ) ),
    inference(paramod_ordered,[status(thm)],[20084,647]) ).

thf(20393,plain,
    ( ( sdtlpdtrp0 @ xN @ xk )
   != slcrc0 ),
    inference(simp,[status(thm)],[20342]) ).

thf(676,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( ( aElementOf0 @ sk1 @ szNzAzT0 )
     != ( aElementOf0 @ sz00 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[240,613]) ).

thf(681,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( sk1 != sz00 )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[676]) ).

thf(684,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO )
    | ( sk1 != sz00 ) ),
    inference(simp,[status(thm)],[681]) ).

thf(273,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ( aElement0 @ ( sk10 @ C @ B @ A ) )
      | ( C
        = ( sdtmndt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ( aElement0 @ ( sk10 @ C @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[273]) ).

thf(290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ~ ( aSet0 @ C )
      | ( sk8 @ A @ B @ C )
      | ( aElement0 @ ( sk10 @ C @ B @ A ) ) ),
    inference(simp,[status(thm)],[289]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( aSubsetOf0 @ B @ A )
        <=> ( ( aSet0 @ B )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ B )
               => ( aElementOf0 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

thf(378,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( ( aSubsetOf0 @ B @ A )
           => ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ B )
                 => ( aElementOf0 @ C @ A ) ) ) )
          & ( ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ B )
                 => ( aElementOf0 @ C @ A ) ) )
           => ( aSubsetOf0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(214,plain,
    ! [A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( isCountable0 @ ( szDzozmdt0 @ A ) )
      | ~ ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) )
      | ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ),
    inference(cnf,[status(esa)],[213]) ).

thf(23075,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
    | ( sdtlseqdt0 @ sz00 @ xk )
    | ( xk != xk ) ),
    inference(paramod_ordered,[status(thm)],[7766,22970]) ).

thf(23076,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
    | ( sdtlseqdt0 @ sz00 @ xk ) ),
    inference(pattern_uni,[status(thm)],[23075:[]]) ).

thf(151,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aSet0 @ B )
      | ~ ( aSet0 @ C )
      | ~ ( aSubsetOf0 @ A @ B )
      | ~ ( aSubsetOf0 @ B @ C )
      | ( aSubsetOf0 @ A @ C ) ),
    inference(cnf,[status(esa)],[150]) ).

thf(9287,plain,
    ( ( aSubsetOf0 @ ( slbdtrb0 @ xk ) @ slcrc0 )
    | ( ( slbdtrb0 @ xk )
     != ( slbdtrb0 @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[137,7914]) ).

thf(9346,plain,
    ( ( aSubsetOf0 @ ( slbdtrb0 @ xk ) @ slcrc0 )
    | ( xk != sz00 ) ),
    inference(simp,[status(thm)],[9287]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
            & ( isCountable0 @ B ) )
         => ( ! [C: $i,D: $i] :
                ( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
                  & ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
                  & ( C != D ) )
               => ( ( sdtlpdtrp0 @ A @ C )
                 != ( sdtlpdtrp0 @ A @ D ) ) )
           => ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgCount) ).

thf(432,plain,
    ! [A: $i] :
      ( ( aFunction0 @ A )
     => ! [B: $i] :
          ( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
            & ( isCountable0 @ B ) )
         => ( ! [C: $i,D: $i] :
                ( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
                  & ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
                  & ( C != D ) )
               => ( ( sdtlpdtrp0 @ A @ C )
                 != ( sdtlpdtrp0 @ A @ D ) ) )
           => ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(177,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( aElementOf0 @ ( sk3 @ B @ A ) @ B )
      | ~ ( sk2 @ A @ B )
      | ( B
        = ( slbdtrb0 @ A ) ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(189,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( aElementOf0 @ ( sk3 @ B @ A ) @ B )
      | ~ ( sk2 @ A @ B ) ),
    inference(lifteq,[status(thm)],[177]) ).

thf(190,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( slbdtrb0 @ A ) )
      | ~ ( aElementOf0 @ A @ szNzAzT0 )
      | ~ ( aSet0 @ B )
      | ( aElementOf0 @ ( sk3 @ B @ A ) @ B )
      | ~ ( sk2 @ A @ B ) ),
    inference(simp,[status(thm)],[189]) ).

thf(13176,plain,
    ( ( xC != xc )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,12868]) ).

thf(13225,plain,
    ( ( xC != xc )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[13176]) ).

thf(59349,plain,
    ( ( xO != szNzAzT0 )
    | ( sk1 != sz00 )
    | ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
     != ( isCountable0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[198,59208]) ).

thf(59420,plain,
    ( ( xO != szNzAzT0 )
    | ( sk1 != sz00 )
    | ( ( slbdtrb0 @ sk1 )
     != xO ) ),
    inference(simp,[status(thm)],[59349]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).

thf(603,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( aSubsetOf0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) @ xT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4182) ).

thf(564,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ( aSubsetOf0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) @ xT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(301,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ( C
       != ( sdtexdt0 @ A @ B ) )
      | ( aFunction0 @ C ) ),
    inference(cnf,[status(esa)],[298]) ).

thf(304,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtexdt0 @ A @ B ) )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ( aFunction0 @ C ) ),
    inference(lifteq,[status(thm)],[301]) ).

thf(305,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ( aFunction0 @ ( sdtexdt0 @ A @ B ) ) ),
    inference(simp,[status(thm)],[304]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ? [B: $i] :
          ( ( aElementOf0 @ B @ xT )
          & ? [C: $i] :
              ( ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ( isCountable0 @ C )
              & ! [D: $i] :
                  ( ( ( aSet0 @ D )
                    & ( aElementOf0 @ D @ ( slbdtsldtrb0 @ C @ xk ) ) )
                 => ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ D )
                    = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4411) ).

thf(326,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ? [B: $i] :
          ( ( aElementOf0 @ B @ xT )
          & ? [C: $i] :
              ( ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ( isCountable0 @ C )
              & ! [D: $i] :
                  ( ( ( aSet0 @ D )
                    & ( aElementOf0 @ D @ ( slbdtsldtrb0 @ C @ xk ) ) )
                 => ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ D )
                    = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(1362,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ ( szDzozmdt0 @ xc ) )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1251,131]) ).

thf(1363,plain,
    aElement0 @ ( sbrdtbr0 @ ( szDzozmdt0 @ xc ) ),
    inference(pattern_uni,[status(thm)],[1362:[bind(A,$thf( szDzozmdt0 @ xc ))]]) ).

thf(4326,plain,
    ( ~ ( isFinite0 @ xS )
    | ( ( aSet0 @ xS )
     != ( aSet0 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[199,4286]) ).

thf(4350,plain,
    ( ~ ( isFinite0 @ xS )
    | ( xS != xO ) ),
    inference(simp,[status(thm)],[4326]) ).

thf(31742,plain,
    ( ( ( slbdtrb0 @ xk )
     != xO )
    | ( ( isFinite0 @ ( slbdtrb0 @ xk ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,19878]) ).

thf(31757,plain,
    ( ( ( slbdtrb0 @ xk )
     != xO )
    | ( ( slbdtrb0 @ xk )
     != xT ) ),
    inference(simp,[status(thm)],[31742]) ).

thf(34837,plain,
    ( ( xN != xe )
    | ( aElementOf0 @ xS @ xS )
    | ( ( szmzizndt0 @ xS )
     != ( szmzizndt0 @ xS ) ) ),
    inference(paramod_ordered,[status(thm)],[5164,34726]) ).

thf(34838,plain,
    ( ( xN != xe )
    | ( aElementOf0 @ xS @ xS ) ),
    inference(pattern_uni,[status(thm)],[34837:[]]) ).

thf(39615,plain,
    ! [A: $i] :
      ( ( xk = sz00 )
      | ( aElementOf0 @ ( sk7 @ A ) @ xT )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[873,259]) ).

thf(39616,plain,
    ( ( xk = sz00 )
    | ( aElementOf0 @ ( sk7 @ ( sk31 @ xk ) ) @ xT ) ),
    inference(pattern_uni,[status(thm)],[39615:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(1729,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( ( szDzozmdt0 @ xc )
     != ( szDzozmdt0 @ xd ) ) ),
    inference(paramod_ordered,[status(thm)],[209,1668]) ).

thf(1742,plain,
    ( ( aSubsetOf0 @ ( szDzozmdt0 @ xc ) @ szNzAzT0 )
    | ( xc != xd ) ),
    inference(simp,[status(thm)],[1729]) ).

thf(274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ( C
       != ( sdtmndt0 @ A @ B ) )
      | ( aSet0 @ C ) ),
    inference(cnf,[status(esa)],[263]) ).

thf(293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sdtmndt0 @ A @ B ) )
      | ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ( aSet0 @ C ) ),
    inference(lifteq,[status(thm)],[274]) ).

thf(294,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSet0 @ A )
      | ~ ( aElement0 @ B )
      | ( aSet0 @ ( sdtmndt0 @ A @ B ) ) ),
    inference(simp,[status(thm)],[293]) ).

thf(1606,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( ( aElementOf0 @ sk1 @ szNzAzT0 )
     != ( aElementOf0 @ sz00 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[240,848]) ).

thf(1639,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( sk1 != sz00 )
    | ( szNzAzT0 != szNzAzT0 ) ),
    inference(simp,[status(thm)],[1606]) ).

thf(1657,plain,
    ( ( aElementOf0 @ ( sk31 @ sk1 ) @ szNzAzT0 )
    | ( aElementOf0 @ sz00 @ xO )
    | ( sk1 != sz00 ) ),
    inference(simp,[status(thm)],[1639]) ).

thf(5092,plain,
    ( ( ( szmzizndt0 @ xS )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 ) ),
    inference(rewrite,[status(thm)],[689,5090]) ).

thf(733,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xK )
     != sk1 )
    | ( ( aElementOf0 @ xK @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
     != ( aElementOf0 @ xK @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,695]) ).

thf(737,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xK )
     != sk1 )
    | ( xK != xK )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[733]) ).

thf(740,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xK )
     != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[737]) ).

thf(59,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aFunction0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( C
            = ( sdtlbdtrb0 @ A @ B ) )
        <=> ( ( aSet0 @ C )
            & ! [D: $i] :
                ( ( aElementOf0 @ D @ C )
              <=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
                  & ( ( sdtlpdtrp0 @ A @ D )
                    = B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).

thf(332,plain,
    ! [A: $i,B: $i] :
      ( ( ( aFunction0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( ( C
              = ( sdtlbdtrb0 @ A @ B ) )
           => ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
                      & ( ( sdtlpdtrp0 @ A @ D )
                        = B ) ) )
                  & ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
                      & ( ( sdtlpdtrp0 @ A @ D )
                        = B ) )
                   => ( aElementOf0 @ D @ C ) ) ) ) )
          & ( ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
                      & ( ( sdtlpdtrp0 @ A @ D )
                        = B ) ) )
                  & ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
                      & ( ( sdtlpdtrp0 @ A @ D )
                        = B ) )
                   => ( aElementOf0 @ D @ C ) ) ) )
           => ( C
              = ( sdtlbdtrb0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(816,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( ( szDzozmdt0 @ xC )
     != ( szDzozmdt0 @ xc ) ) ),
    inference(paramod_ordered,[status(thm)],[454,117]) ).

thf(822,plain,
    ( ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ szNzAzT0 ) @ xT )
    | ( xC != xc ) ),
    inference(simp,[status(thm)],[816]) ).

thf(3885,plain,
    ! [A: $i] :
      ( ( ( szszuzczcdt0 @ sz00 )
        = xK )
      | ( A = sz00 )
      | ( aElementOf0 @ ( sk31 @ A ) @ szNzAzT0 )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[3358,517]) ).

thf(3886,plain,
    ( ( ( szszuzczcdt0 @ sz00 )
      = xK )
    | ( ( sk31 @ xk )
      = sz00 )
    | ( aElementOf0 @ ( sk31 @ ( sk31 @ xk ) ) @ szNzAzT0 ) ),
    inference(pattern_uni,[status(thm)],[3885:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ A )
         => ( aElement0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

thf(442,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ A )
         => ( aElement0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(622,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( xO != szNzAzT0 )
    | ( ( aElementOf0 @ sk1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
     != ( aElementOf0 @ sk1 @ xO ) ) ),
    inference(paramod_ordered,[status(thm)],[101,612]) ).

thf(623,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( xO != szNzAzT0 )
    | ( sk1 != sk1 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO ) ),
    inference(simp,[status(thm)],[622]) ).

thf(624,plain,
    ( ( ( sdtlpdtrp0 @ xe @ sk1 )
     != sk1 )
    | ( xO != szNzAzT0 )
    | ( ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) )
     != xO ) ),
    inference(simp,[status(thm)],[623]) ).

thf(9570,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) )
    | ( xk != xk ) ),
    inference(paramod_ordered,[status(thm)],[7766,7943]) ).

thf(9571,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
    | ( aElement0 @ ( sbrdtbr0 @ ( slbdtrb0 @ sz00 ) ) ) ),
    inference(pattern_uni,[status(thm)],[9570:[]]) ).

thf(22079,plain,
    ( ( aSet0 @ ( slbdtrb0 @ ( sk31 @ xk ) ) )
    | ( aElement0 @ ( sbrdtbr0 @ slcrc0 ) ) ),
    inference(rewrite,[status(thm)],[9571,137]) ).

thf(24496,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( isCountable0 @ ( slbdtrb0 @ sk1 ) )
     != ( isCountable0 @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[362,8213]) ).

thf(24559,plain,
    ( ( xO != szNzAzT0 )
    | ~ ( isFinite0 @ ( slbdtrb0 @ sk1 ) )
    | ( ( slbdtrb0 @ sk1 )
     != szNzAzT0 ) ),
    inference(simp,[status(thm)],[24496]) ).

thf(28966,plain,
    ( ( ( slbdtrb0 @ xK )
     != xS )
    | ( ( isFinite0 @ ( slbdtrb0 @ xK ) )
     != ( isFinite0 @ xT ) ) ),
    inference(paramod_ordered,[status(thm)],[146,19731]) ).

thf(28982,plain,
    ( ( ( slbdtrb0 @ xK )
     != xS )
    | ( ( slbdtrb0 @ xK )
     != xT ) ),
    inference(simp,[status(thm)],[28966]) ).

thf(56,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( aSubsetOf0 @ B @ szNzAzT0 )
        & ( A != slcrc0 )
        & ( B != slcrc0 ) )
     => ( ( ( aElementOf0 @ ( szmzizndt0 @ A ) @ B )
          & ( aElementOf0 @ ( szmzizndt0 @ B ) @ A ) )
       => ( ( szmzizndt0 @ A )
          = ( szmzizndt0 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMinMin) ).

thf(322,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSubsetOf0 @ A @ szNzAzT0 )
        & ( aSubsetOf0 @ B @ szNzAzT0 )
        & ( A != slcrc0 )
        & ( B != slcrc0 ) )
     => ( ( ( aElementOf0 @ ( szmzizndt0 @ A ) @ B )
          & ( aElementOf0 @ ( szmzizndt0 @ B ) @ A ) )
       => ( ( szmzizndt0 @ A )
          = ( szmzizndt0 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(1366,plain,
    ! [A: $i] :
      ( ( aElement0 @ ( sbrdtbr0 @ A ) )
      | ( ( aSet0 @ xO )
       != ( aSet0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[199,131]) ).

thf(1367,plain,
    aElement0 @ ( sbrdtbr0 @ xO ),
    inference(pattern_uni,[status(thm)],[1366:[bind(A,$thf( xO ))]]) ).

thf(215,plain,
    ! [A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( isCountable0 @ ( szDzozmdt0 @ A ) )
      | ~ ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) )
      | ( aElement0 @ ( szDzizrdt0 @ A ) ) ),
    inference(cnf,[status(esa)],[213]) ).

thf(22949,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ xK @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[325,226]) ).

thf(22950,plain,
    sdtlseqdt0 @ xK @ xK,
    inference(pattern_uni,[status(thm)],[22949:[bind(A,$thf( xK ))]]) ).

thf(22980,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ sz00 @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[240,226]) ).

thf(22981,plain,
    sdtlseqdt0 @ sz00 @ sz00,
    inference(pattern_uni,[status(thm)],[22980:[bind(A,$thf( sz00 ))]]) ).

thf(13056,plain,
    ( ( xN != xc )
    | ( ( isFinite0 @ ( szDzozmdt0 @ xc ) )
     != ( isFinite0 @ slcrc0 ) ) ),
    inference(paramod_ordered,[status(thm)],[115,12865]) ).

thf(13107,plain,
    ( ( xN != xc )
    | ( ( szDzozmdt0 @ xc )
     != slcrc0 ) ),
    inference(simp,[status(thm)],[13056]) ).

thf(20361,plain,
    ( ( isCountable0 @ ( sdtlpdtrp0 @ xN @ xk ) )
   != ( isCountable0 @ xT ) ),
    inference(paramod_ordered,[status(thm)],[20084,4360]) ).

thf(20404,plain,
    ( ( sdtlpdtrp0 @ xN @ xk )
   != xT ),
    inference(simp,[status(thm)],[20361]) ).

thf(246,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ( A = slcrc0 )
      | ~ ( aElementOf0 @ B @ A )
      | ~ ( sdtlseqdt0 @ B @ ( sk6 @ B @ A ) )
      | ( B
        = ( szmzizndt0 @ A ) ) ),
    inference(cnf,[status(esa)],[242]) ).

thf(253,plain,
    ! [B: $i,A: $i] :
      ( ( A = slcrc0 )
      | ( B
        = ( szmzizndt0 @ A ) )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ A )
      | ~ ( sdtlseqdt0 @ B @ ( sk6 @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[246]) ).

thf(254,plain,
    ! [B: $i,A: $i] :
      ( ( A = slcrc0 )
      | ( B
        = ( szmzizndt0 @ A ) )
      | ~ ( aSubsetOf0 @ A @ szNzAzT0 )
      | ~ ( aElementOf0 @ B @ A )
      | ~ ( sdtlseqdt0 @ B @ ( sk6 @ B @ A ) ) ),
    inference(simp,[status(thm)],[253]) ).

thf(303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ~ ( aFunction0 @ C )
      | ( ( szDzozmdt0 @ C )
       != B )
      | ( aElementOf0 @ ( sk11 @ C @ B @ A ) @ B )
      | ( C
        = ( sdtexdt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[298]) ).

thf(308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( szDzozmdt0 @ C )
       != B )
      | ( C
        = ( sdtexdt0 @ A @ B ) )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
      | ~ ( aFunction0 @ C )
      | ( aElementOf0 @ ( sk11 @ C @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[303]) ).

thf(309,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtexdt0 @ A @ ( szDzozmdt0 @ B ) )
        = B )
      | ~ ( aFunction0 @ A )
      | ~ ( aSubsetOf0 @ ( szDzozmdt0 @ B ) @ ( szDzozmdt0 @ A ) )
      | ~ ( aFunction0 @ B )
      | ( aElementOf0 @ ( sk11 @ B @ ( szDzozmdt0 @ B ) @ A ) @ ( szDzozmdt0 @ B ) ) ),
    inference(simp,[status(thm)],[308]) ).

thf(20085,plain,
    ! [A: $i] :
      ( ( ( szszuzczcdt0 @ sz00 )
        = xK )
      | ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) )
      | ( ( aElementOf0 @ ( sk31 @ xk ) @ szNzAzT0 )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[3358,218]) ).

thf(20086,plain,
    ( ( ( szszuzczcdt0 @ sz00 )
      = xK )
    | ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( sk31 @ xk ) ) ) ),
    inference(pattern_uni,[status(thm)],[20085:[bind(A,$thf( sk31 @ xk ))]]) ).

thf(22941,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( ( aElementOf0 @ sk1 @ xO )
       != ( aElementOf0 @ A @ szNzAzT0 ) ) ),
    inference(paramod_ordered,[status(thm)],[101,226]) ).

thf(23011,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( sk1 != A )
      | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[22941]) ).

thf(23022,plain,
    ( ( sdtlseqdt0 @ sk1 @ sk1 )
    | ( xO != szNzAzT0 ) ),
    inference(simp,[status(thm)],[23011]) ).

thf(4871,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xk )
      = ( szmzizndt0 @ xS ) )
    | ( ( sdtlpdtrp0 @ xN @ xk )
     != ( sdtlpdtrp0 @ xN @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[594,4711]) ).

thf(4928,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xk )
      = ( szmzizndt0 @ xS ) )
    | ( xN != xN )
    | ( xk != sz00 ) ),
    inference(simp,[status(thm)],[4871]) ).

thf(4940,plain,
    ( ( ( sdtlpdtrp0 @ xe @ xk )
      = ( szmzizndt0 @ xS ) )
    | ( xk != sz00 ) ),
    inference(simp,[status(thm)],[4928]) ).

thf(147484,plain,
    $false,
    inference(cvc4,[status(thm)],[20194,7766,101,34726,14220,1369,138,518,7990,29267,8030,34103,234,9573,115,20056,9351,69974,7368,120,7781,202,3382,4714,59412,4376,217,276,4711,873,3745,22970,32083,797,814,24560,35134,7873,12921,12865,1354,153,1746,34039,39684,68752,417,288,19069,1265,32270,257,320,8025,7914,184,372,587,20059,4349,24558,59208,196,157,38320,7945,18333,284,325,228,316,261,1379,39711,421,20772,152,12864,216,20890,7786,1664,38307,591,321,7376,121,574,19113,18786,821,602,147,280,221,29118,132,42399,660,116,428,32288,133,307,292,248,117,439,20084,39650,59415,12927,220,102,798,7814,201,13104,4557,7703,34898,4375,160,297,192,429,137,165,729,1560,19082,252,19886,456,19731,224,229,8255,566,197,20047,361,7842,3254,156,388,13163,593,141,188,1672,19879,1361,1182,3728,489,7365,69954,225,1659,4721,38100,42554,39632,23078,1744,212,706,42396,647,8219,12859,10834,654,1668,29114,457,129,503,13167,569,134,237,105,7770,508,20290,19878,12361,23086,5090,30911,311,1251,425,824,166,148,1747,161,444,7910,375,513,24557,3358,39888,180,296,149,7372,584,562,423,22945,286,20310,826,12862,204,259,313,144,50265,7875,4573,42546,236,32088,12867,19881,19875,19741,159,31590,113,219,736,31897,3710,509,1175,362,451,4374,208,1571,599,14223,103,594,213,848,240,18912,155,198,108,130,827,695,278,31755,223,135,241,167,455,19734,226,20770,1662,24553,162,374,255,112,553,22953,209,487,7773,123,458,823,194,145,1748,4360,282,4377,150,1743,31845,4346,199,182,20287,19248,31595,20883,127,1658,23084,34101,31269,4145,7779,613,386,1670,28978,314,595,612,69578,154,12868,1749,7374,7784,446,571,143,39763,7844,99,363,203,581,1654,218,104,31871,250,231,4730,34392,32296,517,319,13224,19738,42551,258,158,7840,186,1745,31790,781,7912,114,19077,34402,8253,235,510,39874,207,20393,684,290,119,5164,378,716,214,23076,31912,151,9346,432,146,31786,190,13225,59420,603,168,262,564,305,210,326,239,1363,4350,4286,506,31757,34838,7943,39616,19733,1742,294,136,1657,5092,740,332,8213,822,131,3886,200,691,442,607,624,22079,24559,28982,322,122,1367,215,22950,22981,364,4298,13107,111,20404,254,227,309,20086,23022,454,4940,232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUM600+1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n003.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 06:27:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.99/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.41/1.03  % [INFO] 	 Parsing done (159ms). 
% 1.41/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.86/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.86/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.86/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.07/1.28  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.29  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.30  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.30  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.31  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.31  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.32  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.32  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.33  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.33  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.33  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.07/1.36  % [INFO] 	 Found a conjecture (or negated_conjecture) and 96 axioms. Running axiom selection ... 
% 2.53/1.42  % [INFO] 	 Axiom selection finished. Selected 96 axioms (removed 0 axioms). 
% 2.59/1.44  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.46  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.46  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.46  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.47  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.47  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.47  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.47  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.48  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.48  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.48  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.49  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.59/1.50  % [INFO] 	 Type checking passed. 
% 2.59/1.50  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 90.58/36.86  % External prover 'cvc4' found a proof!
% 90.58/36.86  % [INFO] 	 Killing All external provers ... 
% 90.58/36.86  % Time passed: 36326ms (effective reasoning time: 35819ms)
% 90.58/36.86  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 90.58/36.86  % Axioms used in derivation (96): mDefSel, mFunSort, mZeroNum, mSubASymm, mCardEmpty, m__3533, mImgRng, mSuccLess, mCountNFin, mSegLess, m__4331, mCardSubEx, mDefEmp, m__3435, mFinSubSeg, m__4660, mIHSort, m__3965, mDefSImg, m__4758, mDiffCons, mSubRefl, mDefMin, mSubFSet, mEOfElem, m__3398, mDefDiff, mSelCSet, m__4182, m__3462, mSetSort, mCardS, mSegZero, mSuccEquSucc, m__4730, m__3821, mSelNSet, mDomSet, mSegSucc, mLessSucc, mIH, mFDiffSet, m__3754, mCDiffSet, mFinRel, mSegFin, mDefCons, mNoScLessZr, m__4854, mConsDiff, m__3520, mLessRefl, mLessRel, mDefSeg, mCardSub, mCountNFin_01, m__4891, mCardNum, m__3291, mImgElm, mDefPtt, mImgCount, mLessASymm, mDirichlet, mMinMin, m__4908, mSelFSet, mNatNSucc, mDefMax, m__3453, m__3671, mEmpFin, mLessTotal, mNATSet, mFConsSet, mElmSort, mCardDiff, mZeroLess, mPttSet, mSelSub, mDefSub, mLessTrans, mNatExtra, m__4411, mSuccNum, mSubTrans, m__4618, mCntRel, mSelExtra, m__3418, m__3623, m__4151, mCardCons, mDefRst, mCConsSet, mCardSeg
% 90.58/36.86  % No. of inferences in proof: 932
% 90.58/36.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36326 ms resp. 35819 ms w/o parsing
% 91.04/37.00  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 91.04/37.00  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------